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UNIVERSITY    OF    ILLINOIS    LIBRARY    AT    URBANA-CHAMPAIGN 


LETTERS   OF   EULER 

ON  DIFFERENT   SUBJECTS  IN 

NATURAL    PHILOSOPHY. 

ADDRESSED  TO 

A  GERMAN  PRINCESS. 

WITH    NOTES,    AND   A   LIFE    OF   EULER, 
BY 

DAVID  BREWSTER,  LL.D. 

F.R.S.  LOND.  AND  ED. 

CONTAINING  A   GLOSSARY   OF    SCIENTIFIC   TERMS. 
WITH  ADDITIONAL   NOTES, 

BY  JOHN   GRISCOM,   LL.D. 
IN  TWO   VOLUMES. 

VOL.  II. 


NEW  YORK : 
HARPER  &  BROTHERS, 

NO.    82    CLIFF-STREET. 

1835. 


Entered,  according  to  Act  of  Congress,  in  the  year  1835, 

By  HARPER  &  BROTHERS, 
ID  the  Clerk's  Office  of  the  Southern  District  of  New-York. 


V , 


CONTENTS 

V? 

Ft 

THE    SECOND   VOLUME. 

v 


LETTER  I.  CONTINUATION  of  the  Subject,  and  of  Mis- 
takes in  the  Knowledge  of  Truth  -  -  11 
II.  First  Class  of  known  Truths.  Conviction 
that  Things  exist  externally,  corresponding 
to  the  Ideas  represented  by  the  Senses. 
Objection  of  the  Pyrrhonists.  Reply  -  14 

III.  Another  Objection  of  the  Pyrrhonists  against 

the  Certainty  of  Truths  perceived  by  the 
Senses.  Reply ;  and  Precautions  for  at- 
taining Assurance  of  sensible  Truths  -  17 

IV.  Of  demonstrative,  physical,  and  particularly 

of  moral  Certainty 20 

V.  Remarks  that  the  Senses  contribute  to  the 
Increase  of  Knowledge  ;  and  Precautions 
for  acquiring  the  Certainty  of  historical 

Truths 23 

VI.  Whether  the  Essence  of  Bodies  be  known 

by  us 26 

VII.  The  true  Notion  of  Extension      ...    30 
VIII.  Divisibility  of  Extension  in  infinitum      -        -    33 
IX.  Whether  this  Divisibility  in  infinitum  takes 

place  in  existing  Bodies  -  -  -  -  36 
X.  Of  Monads  -.;...-  -  -  -  -  39 
XI.  Reflections  on  Divisibility  in  infinitum,  and  on 

Monads 42 

XII.  Reply  to  the  Objections  of  the  Monadists  to 

Divisibility  in  infinitum       -        -  -46 

XIII.  Principle  of  the  sufficient  Reason  the  strongest 

Support  of  the  Monadists  -        -        -        -    48 

XIV.  Another  Argument  of  the  Monadists  derived 

from  the  Principle  of  the  sufficient  Reason. 
Absurdities  resulting  from  it*"  -  -  -  52 


CONTENTS. 

XV.  Reflections  on  the  System  of  Monads  -       -  55 

XVI.  Continuation 58 

XVII.  Conclusion  of  Reflections  on  this  System    -  61 

XVIII.  Elucidation  respecting  the  Nature  of  Colours  65 
XIX.  Reflections  on  the  Analogy  between  Colours 

and  Sounds 68 

XX.  Continuation 71 

XXL  How  Opaque  Bodies  are  rendered  visible      -  73 

XXII.  The  Wonders  of  the  human  Voice        -        -  76 

XXIII.  A  Summary  of  the  principal  Phenomena  of 

Electricity 7ft 

XXIV.  The  true  Principle  of  Nature  on  which  are 

founded  all  the  Phenomena  of  Electricity  82 
XXV.  Continuation.     Different  Nature  of  Bodies 

relatively  to  Electricity     -        -        -        -  85 

XXVI.  On  the  same  Subject 88 

XXVII.  Of  positive  and  negative  Electricity.    Expla- 
nation of  the  Phenomenon  of  Attraction    -  92 
XXVIII.  On  the  same  Subject 95 

XXIX.  On  the  electric  Atmosphere          ...  98 

XXX.  Communication  of  Electricity  to  a  Bar  of 

Iron,  by  means  of  a  Globe  of  Glass  -  -  102 
XXXI.  Electrization  of  Men  and  Animals  -  -  106 
XXXII.  Distinctive  Character  of  the  two  Species  of 

Electricity 109 

XXXIII.  How  the  same  Globe  of  Glass  may  furnish  at 

once  the  two  Species  of  Electricity  - 

XXXIV.  The  Leyden  Experiment       -        -        -          115 
XXXV.  Reflections  on  the  Cause  and  Nature  of  Elec- 
tricity, and  on  other  Means  proper  to  pro- 
duce it 119 

XXXVI.  Nature  of  Thunder  :    Explanations  of  the 
ancient  Philosophers,  and  of  DESCARTES. 
Resemblance  of  the  Phenomena  of  Thun- 
der to  those  of  Electricity         -        -        -  122 
XXXVII.  Explanation  of  the  Phenomena  of  Lightning 

and  Thunder     -        -        -        -        -       -  126 

XXXVIII.  Continuation 128 

XXXIX.  The  Possibility  of  preventing  and  of  averting 

the  Effects  of  Thunder     -        -        -        -  131 
XL.  On  the  celebrated  Problem  of  the  Longitude. 
General  Description  of  the  Earth,  of  its 
Axis,  its  two  Poles,  and  the  Equator         -  135 
XLI.  Of  the  Magnitude  of  the  Earth;  of  Meridians, 

and  the  shortest  Road  from  Place  to  Place  139 
XLII.  Of  Latitude,  and  its  Influence  on  the  Sea- 
sons and  the  Length  of  the  Day         -        -  143 
XLIII.  Of  Parallels,  of  the  First  Meridian,  and  of 

Longitude 140 


CONTENTS.  5 

X  LI  V.  Choice  of  the  First  Meridian         -        -        -150 
XLV.  Method  of  determining  the  Latitude,  or  the 

Elevation  of  the  Pole        -        -        -        -  153 
XLVI.  Knowledge  of  the  Longitude  from  a  Calcu- 
lation of  the  Direction  and  of  the  Space 
passed  through  -        -        -  .     -        -        -  157 
XLVII.  Continuation.    Defects  of  this  Method         -  161 
XL VIII.  Second  Method  of  determining  the  Longi- 
tude, by  Means  of  an  exact  Timepiece       -  164 
XLIX.  Continuation,  and  further  Elucidations         -  168 
L.  Eclipses  of  the  Moon  a  third  Method  of  find- 
ing the  Longitude      -  -    '    -        -  171 
LI.  Observation  of  the  Eclipses  of  the  Satellites 
of  Jupiter,  a  fourth  Method  of  finding  the 

Longitude 175 

LII.  The  Motion  of  the  Moon  a  fifth  Method        -  179 
LIII.  Advantages  of  this  last  Method :  its  Degree 

of  Precision 182 

LIV.  On  the  Mariner's  Compass,  and  the  Proper- 
ties of  the  Magnetic  Needle       -        -        -185 
LV.  Declination  of  the  Compass,  and  Manner  of 

observing  it        -        -        -        -        -        -189 

LVI.  Difference  in  the  Declination  of  the  Compass 

at  the  same  Place 192 

LVII.  Chart  of  Declinations ;  Method  of  employing 

it  for  the  Discovery  of  the  Longitude         -  196 
LVIII.  Why  does  the  Magnetic  Needle  affect,  in 
every  Place  of  the  Earth,  a  certain  Direc- 
tion, differing  in  different  Places  ;  and  for 
what  Reason  does  it  change,  with  Time, 

at  the  same  Place  ? 200 

LIX.  Elucidations  respecting  the  Cause  and  Varia- 
tion of  the  Declination  of  Magnetic  Needles  203 
LX.  Inclination  or  Dip  of  Magnetic  Needles        -  207 
LXI.  True  Magnetic   Direction ;    subtile   Matter 

which  produces  the  Magnetic  Power         -  211 
LXII.  Nature  of  the  Magnetic  Matter,  and  of  its 

rapid  Current.    Magnetic  Canals  -  214 

LXIII.  Magnetic  Vortex.    Action  of  Magnets  upon 

each  other •-  218 

LXIV.  Nature  of  Iron  and  Steel.    Method  of  com- 
municating to  them  the  Magnetic  Force    -  221 
LXV.  Action  of  Loadstones  on  Iron.    Phenomena 
observable  on  placing  Pieces  of  Iron  near  a 

Loadstone 226 

LXVI.  Arming  of  Loadstones 230 

LXVII.  Action  and  Force  of  armed  Loadstones         -  234 
LXVIII.  The   Method  of  communicating  to    Steel 
A2 


CONTENTS. 

Letter  j^, 

the  Magnetic  Force,  and  of  magnetizing 
Needles  for  the  Compass.  The  SIMPLE 
TOUCH  ;  its  Defects  ;  Means  of  remedying 
these 238 

LXIX.  On  the  DOUBLE  TOUCH.    Means  of  preserv-" 
ing  the  Magnetic  Matter  in  magnetized 
Bars 241 

LXX.  The  Method  of  Communicating  to  Bars  of 
Steel  a  very  great  Magnetic  Force,  by 
Means  of  other  Bars  which  have  it  in  a 
very  inferior  Degree 246 

LXXI.  Construction  of  artificial  Magnets  in  the  Form 

of  a  Horseshoe  ------  249 

LXXII.  On  Dioptrics.  Instruments  which  that  Sci- 
ence supplies :  of  Telescopes  and  Micro- 
scopes. Different  Figures  given  to  Glasses 

or  Lenses 253 

LXXIII.  Difference  of  Lenses  with  respect  to  the  Curve 
of  their  Surfaces.  Distribution  of  Lenses 
into  three  Classes  ....  257 


LXXIV.  Effect  of  Convex  Lenses 
LXXV.  The  same  Subject.    Distance  of  the  Focus 

of  Convex  Lenses     - 
LXXVI.  Distance  of  the  Image  of  Objects 
LXXVII.  Magnitude  of  Images   - 
LXXVIII.  Burning-glasses    - 


261 

264 
268 
271 

275 

278 


LXXIX.  The  Camera  Obscura    -        ... 
LXXX.  Reflections  on   the  Representation   in   the 

Camera  Obscura        -        -        ...  283 
LXXXI.  Of  the  Magic  Lantern,  and  Solar  Micro- 
scope  286 

LXXXII.  Use  and  Effect  of  a  simple  convex  Lens  -  290 
LXXXIII.  Use  and  Effect  of  a  concave  Lens  -  -  293 
LXXXIV.  Of  apparent  Magnitude,  of  the  Visual  Angle, 

and  of  Microscopes  in  general   -  297 

LXXXV.  Estimation   of  the    Magnitude    of  Objects 

viewed  through  the  Microscope         -        -  300 
LXXXVI.  Fundamental  Proposition  for  the  Construc- 
tion of  simple  Microscopes.    Plan  of  some 
simple  Microscopes    -----  304 
LXXX VII.  Limits  and  Defects  of  the  simple  Microscope  307 
LXXX VIII.  On  Telescopes,  and  their  Effect    -        -        -  311 

LXXXIX.  Of  Pocket-glasses 314 

XC.  On  the  magnifying  Power  of  Pocket-glasses  318 
XCI.  Defects  of  Pocket-glasses.    Of  the  apparent 

Field -       -  322 


CONTENTS.  7 

Letter  Page 

XCII.  Determination  of  the   apparent    Field  for 

Pocket-glasses  ------  326 

XCIII.  Astronomical  Telescopes,  and  their  magnify- 
ing Power 329 

XCIV.  Of  the  apparent  Field,  and  the  Place  of  the 

Eye 332 

XCV.  Determination  of  the  magnifying  Power  ot 
Astronomical  Telescopes,  and  the  Con- 
ctruction  of  a  Telescope  which  shall  mag- 
nify Objects  a  given  Number  of  Times  -  336 

XCVI.  Degree  of  Clearness 339 

XCVH.  Aperture  of  Object-glasses    -        -       -        -  343 

XCVIII.  On  Distinctness  in  the  Expression.    On  the 
Space    of   Diffusion   occasioned   by   the 
Aperture  of  Object-glasses,  and  considered 
as  the  first  Source  of  Want  of  Distinctness 
in  the  Representation        -  347 

XCIX.  Diminution  of  the  Aperture  of  Lenses,  and 
other  Means  of  lessening  the  Space  of 
Diffusion,  till  it  is  reduced  to  Nothing       -  351 
C.  Of  compound  Object-glasses         -  -  355 

CI.  Formation  of  simple  Object-glasses      -        -  358 
CII.  Second  Source  of  Defect   as   to  Distinct- 
ness of  Representation  by  the  Telescope. 
Different  Refrangibility  of  Rays        -        -  362 
Cm.  Means  of  remedying  this  Defect  by  compound 

Object-glasses    -        -        -        -        -        -  366 

CIV.  Other  Means  more  practicable      ...  369 
CV.  Recapitulation  of  the  Qualities  of  a  good 

Telescope 373 

CVI.  Terrestrial  Telescopes  with  four  Lenses      -  376 
CVII.  Arrangement  of  Lenses  in  Terrestrial  Tele- 
scopes         379 

CVIII.  Precautions  to  be  observed  in  the  Construc- 
tion of  Telescopes.  Necessity  of  blacken- 
ing the  Inside  of  Tubes.  Diaphragms  -  382 
CIX.  In  what  Manner  Telescopes  represent  the 
Moon,  the  Planets,  the  Sun,  and  the  fixed 
Stars.  Why  these  last  appear  smaller 
through  the  Telescope  than  to  the  naked 
Eye.  Calculation  of  the  Distance  of  the 
fixed  Stars,  from  a  Comparison  of  their 
apparent  Magnitude  with  that  of  the  Sun  385 
CX.  Why  do  the  Moon  and  the  Sun  appear  greater 
at  rising  and  setting  than  at  a  certain  Ele- 
vation? Difficulties  attending  the  Solu- 
tion of  this  Phenomenon  ....  388 


CONTENTS. 

Letter  Page 

CXI.  Reflections  on  the  Question  respecting  the 
Moon's  apparent  Magnitude.  Progress 
towards  a  Solution  of  the  Difficulty.  Ab- 
surd Explanation 391 

CXII.  An  Attempt  towards  the  true  Explanation  of 
this  Phenomenon  :  the  Moon  appears  more 
distant  when  in  the  Horizon  than  when  at 
a  great  Elevation 395 

CXIII.  The  Heavens  appear  under  the  Form  of  an 

Arch  flattened  towards  the  Zenith     -        -  398 

CXIV.  Reason  assigned  for  the  Faintness  of  the 

Light  of  Heavenly  Bodies  in  the  Horizon    401 
CXV.  Illusion  respecting  the  Distance  of  Objects, 

and  the  Diminution  of  Lustre   -        -        -  405 

CXVI.  On  the  Azure  Colour  of  the  Heavens   -        -  407 
CXVII.  What  the  Appearance  would  be  were  the  Air 

perfectly  transparent  -----  410 
CXVIII.  Refraction  of  Rays  of  Light  in  the  Atmo- 
sphere, and  its  Effects.    Of  the  Twilight. 
Of  the  apparent  Rising  and  Setting  of  the 
Heavenly  Bodies 414 

CXIX.  The  Stars  appear  at  a  greater  Elevation  than 

they  are.    Table  of  Refractions        -       -417 


LETTERS 

ON 

DIFFERENT  SUBJECTS 

IN 

NATURAL  PHILOSOPHY. 


LETTER  I. 

Continuation  of  the   Subject,  and  of  Mistakes  in  the 
Knowledge  of  Truth. 

THE  three  classes  of  truths  which  I  have  now  un- 
folded are  tjje  only  sources  of  all  our  knowledge ; 
all  being  derived  from  our  own  experience,  from 
reasoning,  or  from  the  report  of  others. 

It  is  not  easy  to  determine  which  of  these  three 
sources  contributes  most  to  the  increase  of  know- 
ledge. Adam  and  Eve  must  have  derived  theirs 
chiefly  from  the  two  first ;  God,  however,  revealed 
many  things  to  them,  the  knowledge  of  which  is  to 
be  referred  to  the  third  source,  as  neither  their  own 
experience  nor  their  powers  of  reasoning  could 
have  conducted  them  so  far. 

Without  recurring  to  a  period  so  remote,  we  are 
sufficiently  convinced,  that  if  we  were  determined  to 
believe  nothing  of  what  we  hear  from  others,  or  read 
in  their  writings,  we  should  be  in  a  state  of  almost 
total  ignorance.  It  is  very  far,  however,  from  being 
our  duty  to  believe  every  thing  that  is  said,  or  that 


12  MISTAKES   IN   THE 

we  read.  We  ought  constantly  to  employ  our  dis- 
cerning faculties,  not  only  with  respect  to  truths  of 
the  third  class,  but  likewise  of  the  two  others. 

We  are  so  liable  to  suffer  ourselves  to  be  dazzled 
by  the  senses,  and  to  mistake  in  our  reasonings,  that 
the  very  sources  laid  open  by  the  Creator  for  the 
discovery  of  truth  very  frequently  plunge  us  into 
error.  Notions  of  the  third  class,  therefore,  ought 
not  in  reason  to  fall  under  suspicion,  any  more  than 
such  as  belong  to  the  other  two.  We  ought,  there- 
fore, to  be  equally  on  our  guard  against  deception, 
whatever  be  the  class  to  which  the  notion  belongs ; 
for  we  find  as  many  instances  of  error  in  the  first 
and  second  classes  as  in  the  third.  The  same  thing 
holds  with  regard  to  the  certainty  of  the  particular 
articles  of  knowledge  which  these  three  sources  sup- 
ply ;  and  it  cannot  be  affirmed  that  the  truths  of  any 
one  order  have  a  surer  foundation  than  those  of 
another.  Each  class  is  liable  to  errors,  by  which  we 
may  be  misled ;  but  there  are  likewise  precautions 
which,  carefully  observed,  furnish  us  with  nearly 
the  same  degree  of  conviction.  I  do  not  know 
whether  you  are  more  thoroughly  convinced  of  this 
truth,  that  two  triangles  which  have  the  same  base 
and  the  same  height  are  equal  to  one  another,  than 
of  this,  that  the  Russians  have  been  at  Berlin; 
though  the  former  is  founded  on  a  chain  of  accurate 
reasoning,  whereas  the  latter  depends  entirely  on 
the  veracity  of  your  informer. 

Respecting  the  truths,  therefore,  of  each  of  these 
classes,  we  must  rest  satisfied  with  such  proofs  as 
correspond  to  their  nature ;  and  it  would  be  ridicu- 
lous to  insist  upon  a  geometrical  demonstration  of 
the  truths  of  experience,  or  of  history.  This  is 
usually  the  fault  of  those  who  make  a  bad  use  of  their 
penetration  in  intellectual  truths,  to  require  mathe- 
matical demonstration  in  proof  of  all  the  truths  of 
religion,  a  great  part  of  which  belongs  to  the  third 
class. 


KNOWLEDGE    OF    TRUTH.  13 

There  are  persons  determined  to  believe  and  admit 
nothing  but  what  they  see  and  touch ;  whatever  you 
would  prove  to  them  by  reasoning,  be  it  ever  so  solid, 
they  are  disposed  to  suspect,  unless  you  place  it 
before  their  eyes.  Chymists,  anatomists,  and  nat- 
ural philosophers,  who  employ  themselves  wholly 
in  making  experiments,  are  most  chargeable  with 
this  fault.  Every  thing  that  the  one  cannot  melt  in 
his  crucible,  or  the  other  dissect  with  his  scalpel, 
they  reject  as  unfounded.  To  no  purpose  would  you 
speak  to  them  of  the  qualities  and  nature  of  the  soul ; 
they  admit  nothing  but  what  strikes  the  senses. 

Thus,  the  particular  kind  of  study  to  which  every 
one  is  addicted  has  such  a  powerful  influence  on  his 
manner  of  thinking,  that  the  natural  philosopher 
and  chymist  will  have  nothing  but  experiments,  and 
the  geometrician  and  logician  nothing  but  argu- 
ments; which  constitute,  however,  proofs  entirely 
different,  the  one  attached  to  the  first  class,  the 
other  to  the  second,  which  ought  always  to  be  care- 
fully distinguished,  according  to  the  nature  of  the 
objects. 

But  can  it  be  possible  that  persons  should  exist 
who,  wholly  absorbed  in  pursuits  pertaining  to  the 
third  class,  call  only  for  proofs  derived  from  that 
source  1  I  have  known  some  of  this  description,  who, 
totally  devoted  to  the  study  of  history  and  antiquity, 
would  admit  nothing  as  true  but  what  you  could 
prove  by  history,  or  the  authority  of  some  ancient 
author.  They  perfectly  agree  with  you  respecting 
the  truth  of  the  propositions  of  Euclid,  but  merely 
on  the  authority  of  that  author,  without  paying  any 
attention  to  the  demonstrations  by  which  he  sup- 
ports them  ;  they  even  imagine  that  the  contrary  of 
these  propositions  might  be  true,  if  the  ancient  geome- 
tricians had  thought  proper  to  maintain  it. 

This  is  a  source  of  error  which  retards  many  in 
the  pursuit  of  truth;  but  we  find  it  rather  among 
the  learned,  than  among  those  who  are  beginning  to 

VOL.  II.— B 


14  OBJECTION    OF    THE    PYRRHONISTS. 

apply  themselves  to  the  study  of  the  sciences.  We 
ought  to  have  no  predilection  in  favour  of  any  one 
of  the  three  species  of  proofs  which  each  class  re- 
quires; and  provided  they  are  sufficient  in  their 
kind,  we  are  bound  to  admit  them. 

I  have  seen  or  felt,  is  the  proof  of  the  first  class. 
/  can  demonstrate  it,  is  that  of  the  second :  we  like- 
wise say,  I  know  it  is  so.  Finally,  /  receive  it  on  the 
testimony  of  persons  worthy  of  credit,  or  I  believe  it 
on  solid  grounds,  is  the  proof  of  the  third  class. 

4th  April,  1761. 


LETTER  II. 

First  Class  of  known  Truths.  Conviction  that  Things 
exist  externally,  corresponding  to  the  Ideas  repre- 
sented by  the  Senses.  Objection  of  the  Pyrrhonists. 
Reply. 

WE  include  in  the  first  class  of  known  truths 
those  which  we  acquire  immediately  by  means  of 
the  senses.  I  have  already  remarked,  that  they  not 
only  supply  the  soul  with  certain  representations  re- 
lative to  the  changes  produced  in  a  part  of  the  brain; 
but  that  they  excite  there  a  conviction  of  the  real 
existence  of  things  external,  corresponding  to  the 
ideas  which  the  senses  present  to  us. 

The  soul  is  frequently  compared  to  a  man  shut  up 
m  a  dark  room,  in  which  the  images  of  external  ob- 
jects are  represented  on  the  wall  by  means  of  a  glass. 
This  comparison  is  tolerably  just,  as  far  as  it  respects 
the  man  looking  at  the  images  on  the  wall ;  for  this 
act  is  sufficiently  similar  to  that  of  the  soul,  contem- 
plating the  impressions  made  in  the  brain ;  but  the 
comparison  appears  to  me  extremely  defective,  as 
far  as  it  respects  the  conviction  that  the  objects 
which  occasion  these  images  really  exist. 

The  man  in  the  dark  room  will  immediately  sus- 


OBJECTION    OF    THE    PYRRHONISTS.  15 

pect  the  existence  of  these  objects ;  and  if  he  has 
no  doubt  about  the  matter,  it  is  because  he  has  been 
out  of  doors,  and  has  seen  them ;  besides  this, 
knowing  the  nature  of  his  glass,  he  is  assured  that 
nothing  can  be  represented  on  the  wall  but  the  im- 
ages of  the  objects  which  are  without  the  chamber 
before  the  glass.  But  this  is  not  the  case  with  the 
soul ;  it  has  never  quitted  its  place  of  residence  to 
contemplate  the  objects  themselves  ;  and  it  knows 
still  less  the  construction  of  the  sensitive  organs, 
and  the  nerves  which  terminate  in  the  brain.  It  is 
nevertheless  much  more  powerfully  convinced  of 
the  real  existence  of  objects  than  our  man  in  the 
dark  room  possibly  can  be.  I  am  apprehensive  of 
no  objection  on  this  subject,  the  thing  being  too  clear 
of  itself  to  admit  any,  though  we  do  not  know  the 
true  foundation  of  it.  No  one  ever  entertained  any 
doubt  about  it,  except  certain  visionaries  who  have 
bewildered  themselves  in  their  own  reveries. 
Though  they  say  that  they  doubt  the  existence  of 
external  objects,  they  entertain  no  such  doubt  in 
fact;  for  why  would  they  have  affirmed  it,  unless 
they  had  believed  the  existence  of  other  men,  to 
whom  they  wished  to  communicate  their  extrava- 
gant opinions. 

This  conviction  respecting  the  existence  of  the 
things  whose  images  the  senses  represent,  appears 
not  only  in  men  of  every  age  and  condition,  but 
likewise  in  all  animals.  The  dog  which  barks  at  me 
has  no  doubt  of  my  existence,  though  his  soul  per- 
ceives but  a  slight  image  of  my  person.  Hence  I 
conclude,  that  this  conviction  is  essentially  con- 
nected with  our  sensations,  and  that  the  truths  which 
the  senses  convey  to  us  are  as  well  founded  as  the 
most  undoubted  truths  of  geometry. 

Without  this  conviction  no  human  society  could 
subsist,  for  we  should  be  continually  falling  into  the 
greatest  absurdities,  and  the  grossest  contradictions. 

Were  the  peasantry  to  dream  of  doubting  about 


16  OBJECTION    OF    THE    PYRRHONISTS. 

the  existence  of  their  bailiff,  or  soldiers  about  that 
of  their  officers,  into  what  confusion  should  we  be 
plunged  !  Such  absurdities  are  entertained  only  by 
philosophers  ;  any  other  giving  himself  up  to  them 
would  be  considered  as  having  lost  his  reason.  Let 
us  then  acknowledge  this  conviction  as  one  of  the 
principal  laws  of  nature,  and  that  it  is  complete, 
though  we  are  absolutely  ignorant  of  its  true  rea- 
sons, and  very  far  from  being  able  to  explain  them 
in  an  intelligible  manner. 

However  important  this  reflection  may  be,  it  is 
by  no  means,  however,  exempted  from  difficulties ; 
but  were  they  ever  so  great,  and  though  it  might  be 
impossible  for  us  to  solve  them,  they  do  not  in  the 
smallest  degree  affect  the  truth  which  I  have  just  es- 
tablished, and  which  we  ought  to  consider  as  the 
most  solid  foundation  of  human  knowledge. 

It  must  be  allowed  that  our  senses  sometimes  de- 
ceive us ;  and  hence  it  is  that  those  subtile  philoso- 
phers who  value  themselves  on  doubting  of  every 
thing  deduce  the  consequence,  that  we  ought  never 
to  depend  on  our  senses.  I  have  perhaps  oftener 
than  once  met  an  unknown  person  in  the  street, 
whom  I  mistook  for  an  acquaintance :  as  I  was  de- 
ceived in  that  instance,  nothing  prevents  my  being 
always  deceived ;  and  I  am,  therefore,  never  assured 
that  the  person  to  whom  I  speak  is  in  reality  the 
one  1  imagine. 

Were  I  to  go  to  Magdeburg,  and  to  present  my- 
self to  your  highness,  I  ought  always  to  be  appre- 
hensive of  grossly  mistaking :  nay,  perhaps  I  should 
not  be  at  Magdeburg,  for  there  are  instances  of  a 
man's  sometimes  taking  one  city  for  another.  It  is 
even  possible  I  may  never  have  had  the  happiness 
of  seeing  you,  but  was  always  under  the  power  of 
delusion  when  I  thought  myself  to  be  enjoying  that 
felicity. 

Such  are  the  natural  consequences  resulting  from 
the  sentiments  of  certain  philosophers ;  and  you 


OBJECTION    OF    THE    PYRRHONISTS.  17 

must  be  abundantly  sensible  that  they  not  only  lead 
to  manifest  absurdity,  but  have  a  tendency  to  dis- 
solve all  the  bonds  of  society. 
7th  April,  1761. 

LETTER  III. 

Another  Objection  of  the  Pyrrhonists  against  the  Cer- 
tainty of  Truths  perceived  by  the  Senses.  Reply  ; 
and  Precautions  for  attaining  Assurance  of  Sensible 
Truths. 

THOUGH  the  objection  raised  against  the  certainty 
of  truths  perceived  by  the  senses,  of  which  I  have 
been  speaking,  may  appear  sufficiently  powerful,  at- 
tempts have  been  made  to  give  it  additional  support 
from  the  well-known  maxim,  that  we  ought  never  to 
trust  him  who  has  once  deceived  us.  A  single  ex- 
ample, therefore,  of  mistake  in  the  senses,  is  suf- 
ficient to  destroy  all  their  credit.  If  this  objection  is 
well  founded,  it  must  be  admitted  that  human  soci- 
ety is,  of  course,  completely  subverted. 

By  way  of  reply,  I  remark,  that  the  two  other 
sources  of  knowledge  are  subject  to  difficulties  of  a 
similar  nature,  nay,  perhaps  still  more  formidable. 
How  often  are  our  reasonings  erroneous !  I  venture 
to  affirm,  that  we  are  much  more  frequently  de- 
ceived by  these  than  by  our  senses.  But  does  it 
follow  that  our  reasonings  are  always  fallacious,  and 
that  we  can  have  no  dependence  on  any  truth  dis- 
covered to  us  by  the  understanding  1  It  must  be  a 
matter  of  doubt,  then,  whether  two  and  two  make 
four,  or  whether  the  three  angles  of  a  triangle  be 
equal  to  two  right  angles  ;  it  would  even  be  ridicu- 
lous to  pretend  that  this  should  pass  for  truth. 
Though,  therefore,  men  may  have  frequently  rea- 
soned inconclusively,  it  would  be  almost  absurd  to 
B2 


18  ANOTHER    OBJECTION   OF 

infer  that  there  are  not  many  intellectual  truths  of 
which  we  have  the  most  complete  conviction. 

The  same  remark  applies  to  the  third  source  of 
human  knowledge,  which  is  unquestionably  the  most 
subject  to  error.  How  often  have  we  been  deceived 
by  a  groundless  rumour,  or  false  report,  respecting 
certain  events  !  And  who  would  be  so  weak  as  to 
believe  all  that  gazetteers  and  historians  have  writ- 
ten ?  At  the  same  time,  whoever  should  think  of 
maintaining  that  every  thing  related  or  written  by 
others  is  false  would  undoubtedly  fall  into  greater 
absurdities  than  the  person  who  believed  every  thing. 
Accordingly,  notwithstanding  so  many  groundless 
reports  and  false  testimonies,  we  are  perfectly  assured 
of  the  truth  of  numberless  facts,  of  which  we  have 
no  evidence  but  testimony. 

There  are  certain  characters  which  enable  us  to 
distinguish  truth ;  and  each  of  the  three  sources  has 
characters  peculiar  to  itself.  When  my  eyes  have 
deceived  me,  in  mistaking  one  man  for  another,  I 
presently  discover  my  error:  it  is  evident,  there- 
fore, that  precautions  may  be  used  for  the  prevention 
of  error.  If  there  were  not,  it  would  be  impossible 
ever  to  perceive  that  we  had  been  deceived.  Those, 
then,  who  maintain  that  we  so  often  deceive  our- 
selves are  obliged  to  admit  that  it  is  possible  for  us 
to  perceive  we  have  been  deceived,  or  they  must  ac- 
knowledge that  they  themselves  are  deceived  when 
they  charge  us  with  error. 

It  is  remarkable,  that  truth  is  so  well  established 
that  the  most  violent  propensity  to  doubt  of  every 
thing  must  come  to  this,  in  spite  of  itself.  There- 
fore, as  logic  prescribes  rules  for  just  reasoning,  the 
observance  of  which  will  secure  us  from  error, 
where  intellectual  truth  is  concerned;  there  are 
likewise  certain  rules,  as  well  for  the  first  source, 
that  of  our  senses,  as  for  the  third,  that  of  belief 

The  rules  of  the  first  are  so  natural  to  us,  that  all 
men,  the  most  stupid  not  excepted,  understand  and 


THE    PYRRHONISTS.  19 

practise  them  much  better  than  the  greatest  scholars 
are  able  to  describe  them.  Though  it  may  be  easy 
sometimes  to  confound  a  clown,  yet  when  the  hail 
destroys  his  crop,  or  the  thunder  breaks  upon  his 
cottage,  the  most  ingenious  philosopher  will  never 
persuade  him  that  it  was  a  mere  illusion  ;  and  every 
man  of  sense  must  admit  that  the  country-fellow  is 
in  the  right,  and  that  he  is  not  always  the  dupe  of 
the  fallaciousness  of  his  senses.  The  philosopher 
may  be  able,  perhaps,  to  perplex  him  to  such  a  de- 
gree that  he  shall  be  unable  to  reply ;  but  he  will 
inwardly  treat  all  the  fine  reasonings  which  at- 
tempted to  confound  him  with  the  utmost  scorn. 
The  argument,  that  the  senses  sometimes  deceive 
us,  will  make  but  a  very  slight  impression  on  his 
mind ;  and  when  he  is  told,  with  the  greatest  elo- 
quence, that  every  thing  the  senses  represent  to  us 
has  no  more  reality  than  the  visions  of  the  night,  it 
will  only  provoke  laughter. 

But  if  the  clown  should  pretend  to  play  the  phi- 
losopher in  his  turn,  and  maintain  that  the  bailiff  is 
a  mere  phantom,  and  that  all  who  consider  him  as 
something  real,  and  submit  to  his  authority,  are 
fools;  this  sublime  philosophy  would  be  in  a  mo- 
ment overturned,  and  the  leader  of  the  sect  soon 
made  to  feel,  to  his  cost,  the  force  of  the  proofs  which 
the  bailiff  could  give  him  of  the  reality  of  his  ex- 
istence. 

You  must  be  perfectly  satisfied,  then,  that  there 
are  certain  characters  which  destroy  every  shadow 
of  doubt  respecting  the  reality  and  truth  of  what  we 
know  by  the  senses ;  and  these  same  characters  are 
so  well  known,  and  so  strongly  impressed  on  our 
minds,  that  we  are  never  deceived  when  we  employ 
the  precautions  necessary  to  that  effect.  But  it  is 
extremely  difficult  to  make  an  exact  enumeration  of 
these  characters,  and  to  explain  their  nature.  We 
commonly  say,  that  the  sensitive  organs  ought  to  be 
in  a  good  natural  state ;  that  the  air  ought  not  to  be 


20  DEMONSTRATIVE,   PHYSICAL, 

obscured  by  a  fog ;  finally,  that  we  must  employ  a 
sufficient  degree  of  attention,  and  endeavour,  above 
all  things,  to  examine  the  same  object  by  two  or 
more  of  our  senses  at  once.  But  I  am  firmly  per- 
suaded that  every  one  knows,  and  puts  in  practice, 
rules  much  more  solid  than  any  which  could  be  pre- 
scribed to  him. 
llth  April,  1761. 


LETTER  IV, 

Of  Demonstrative,  Physical,  and  particularly  of  Moral 
Certainty. 

THERE  are,  therefore,  three  species  of  knowledge 
which  we  must  consider  as  equally  certain,  provided 
we  employ  the  precautions  necessary  to  secure  us 
against  error.  And  hence  likewise  result  three 
species  of  certainty. 

The  first  is  called  physical  certainty.  When  I  am 
convinced  of  the  truth  of  any  tiling,  because  1  myself 
have  seen  it,  I  have  a  physical  certainty  of  it ;  and 
if  I  am  asked  the  reason,  I  answer,  that  my  own 
senses  give  me  full  assurance  of  it,  and  that  I  am, 
or  have  been,  an  eyewitness  of  it.  It  is  thus  I 
know  that  Austrians  have  been  at  Berlin,  and  that 
some  of  them  committed  great  irregularities  there. 
I  know,  in  the  same  manner,  that  fire  consumes  all 
combustible  substances ;  for  I  myself  have  seen  it, 
and  I  have  a  physical  certainty  of  its  truth. 

The  certainty  which  we  acquire  by  a  process  of 
reasoning  is  called  logical  or  demonstrative  certainty, 
because  we  are  convinced  of  its  truth  by  demonstra- 
tion. The  truths  of  geometry  mayliere  be  produced 
as  examples,  and  it  is  logical  certainty  which  gives  us 
the  assurance  of  them. 

Finally,  the  certainty  which  we  have  of  the  truth 
of  what  we  know  only  by  the  report  of  others  is 


AND   MORAL    CERTAINTY.  21 

called  moral  certainty,  because  it  is  founded  on  the 
credibility  of  the  persons  who  make  the  report.  Thus 
you  have  only  a  moral  certainty  that  the  Russians 
have  been  at  Berlin ;  and  the  same  thing  applies  to 
all  historical  facts.  We  know  with  a  moral  certainty 
that  there  was  formerly  at  Rome  a  Julius  Caesar, 
an  Augustus,  a  Nero,  &c.,  and  the  testimonies 
respecting  these  are  so  authentic,  that  we  are  as 
fully  convinced  of  them  as  of  the  truths  which  we 
discover  by  our  senses,  or  by  a  chain  of  fair  rea- 
soning. 

We  must  take  care,  however,  not  to  confound 
these  three  species  of  certainty — physical,  logical, 
and  moral — each  of  which  is  of  a  nature  totally  dif- 
ferent from  the  others.  I  propose  to  treat  of  each 
separately ;  and  shall  begin  with  a  more  particular 
explanation  of  moral  certainty,  which  is  the  third 
species. 

It  is  to  be  attentively  remarked,  that  this  third 
source  divides  into  two  branches,  according  as  others 
simply  relate  what  they  themselves  have  seen,  or 
made  full  proof  of  by  their  senses,  or  as  they  com- 
municate to  us,  together  with  these,  their  reflections 
and  reasonings  upon  them.  We  might  add  still  a 
third  branch,  wThen  they  relate  what  they  have  heard 
from  others. 

As  to  this  third  branch,  it  is  generally  allowed  to 
be  very  liable  to  error,  and  that  a  witness  is  to  be 
believed  only  respecting  what  he  himself  has  seen  or 
experienced.  Accordingly,  in  courts  of  justice,  when 
witnesses  are  examined,  great  care  is  taken  to  dis- 
tinguish, in  their  declarations,  what  they  themselves 
have  seen  and  experienced,  from  what  they  fre- 
quently add  of  their  reflections  and  reasonings  upon 
it.  Stress  is  laid  only  on  what  they  themselves  have 
seen  or  experienced ;  but  their  reflections,  and  the 
conclusions  which  they  draw,  however  well  founded 
they  may  otherwise  be,  are  entirely  set  aside.  The 
same  maxim  is  observed  with  respect  to  historians ; 


22      PHYSICAL  AND  MORAL  CERTAINTY. 

and  we  wish  them  to  relate  only  what  they  them- 
selves have  witnessed,  without  pursuing  the  reflec- 
tions which  they  so  frequently  annex,  though  these 
may  be  a  great  ornament  to  history.  Thus  we  have 
a  greater  dependence  on  the  truth  of  what  others 
have  experienced  by  their  own  senses,  than  on  what 
they  have  discovered  by  pursuing  their  meditations. 
Every  one  wishes  to  be  master  of  his  own  judgment ; 
and  unless  he  himself  feels  the  foundation  and  the 
demonstration,  he  is  not  persuaded. 

Euclid  would  in  vain  have  announced  to  us  the 
most  important  truths  of  geometry ;  we  should  never 
have  believed  him  on  his  word,  but  have  insisted 
on  prosecuting  the  demonstration  step  by  step  our- 
selves. If  I  were  to  tell  you  that  I  had  seen  such 
or  such  a  thing,  supposing  my  report  faithful,  you 
would  without  hesitation  give  credit  to  it;  nay,  I 
should  be  very  much  mortified  if  you  were  to  sus- 
pect me  of  falsehood.  But  when  I  inform  you  that 
in  a  right-angled  triangle,  the  squares  described  on 
the  two  smaller  sides  are  together  equal  to  the  square 
of  the  greater  side,  I  do  not  wish  to  be  believed  on 
my  word,  though  I  am  as  much  convinced  of  it  as 
it  is  possible  to  be  of  any  thing ;  and  though  I  could 
allege,  to  the  same  purpose,  the  authority  of  the 
greatest  geniuses  who  have  had  the  same  conviction, 
I  should  rather  wish  you  to  discredit  my  assertion, 
and  to  withhold  your  assent,  till  you  yourself  com- 
prehended the  solidity  of  the  reasonings  on  which 
the  demonstration  is  founded. 

It  does  not  follow,  however,  that  physical  cer- 
tainty, or  that  which  the  senses  supply,  is  greater 
than  logical  certainty,  founded  on  reasoning;  but 
whenever  a  truth  of  this  species  presents  itself,  it  is 
proper  that  the  mind  should  give  close  application 
to  it,  and  become  master  of  the  demonstration. 
This  is  the  best  method  of  cultivating  the  sciences, 
and  of  carrying  them  to  the  highest  degree  of  per- 
fection. 


INCREASE    OF   KNOWLEDGE.  23 

The  truths  of  the  senses,  and  of  history,  greatly 
multiply  the  particulars  of  human  knowledge ;  but 
the  faculties  of  the  mind  are  put  in  action  only  by 
reflection  or  reasoning. 

We  never  stop  at  the  simple  evidence  of  the 
senses,  or  the  facts  related  by  others ;  but  always 
follow  them  up  and  blend  them  with  reflections  of 
our  own :  we  insensibly  supply  what  seems  deficient, 
by  the  addition  of  causes  and  motives,  and  the  de- 
duction of  consequences.  It  is  extremely  difficult, 
for  this  reason,  in  courts  of  justice,  to  procure  sim- 
ple unblended  testimony,  such  as  contains  what  the 
witnesses  actually  saw  and  felt,  and  no  more ;  for 
witnesses  ever  will  be  mingling  their  own  reflections, 
without  perceiving  that  they  are  doing  so. 

Uth  April,  1761. 


LETTER  V. 

Remarks  that  the  Senses  contribute  to  the  Increase  of 
Knowledge;  and  Precautions  for  acquiring  the  Cer- 
tainty of  Historical  Truths. 

THE  knowledge  supplied  by  our  senses  is  un- 
doubtedly the  earliest  which  we  acquire  ;  and  upon 
this  the  soul  founds  the  thoughts  and  reflections 
which  discover  to  it  a  great  variety  of  intellectual 
truths.  In  order  the  better  to  comprehend  how  the 
senses  contribute  to  the  advancement  of  knowledge, 
I  begin  with  remarking,  that  the  senses  act  only  on 
individual  things,  which  actually  exist  under  circum- 
stances determined  or  limited  on  all  sides. 

Let  us  suppose  a  man  suddenly  placed  in  the 
world,  possessed  of  all  his  faculties,  but  entirely  des- 
titute of  experience  ;  let  a  stone  be  put  in  his  hand, 
let  him  then  open  that  hand,  and  observe  that  the 
stone  falls.  This  is  an  experiment  limited  on  all 
sides,  which  gives  him  no  information,  except  that 


24  THE    SENSES   CONTRIBUTE    TO 

this  stone,  being  in  the  left  hand,  for  example,  and 
dropped,  falls  to  the  ground;  he  is  by  no  means 
absolutely  certain  that  the  same  effect  would  ensue 
were  he  to  take  another  stone,  or  the  same  stone, 
with  his  right  hand.  It  is  still  uncertain  whether 
this  stone,  under  the  same  circumstances,  would 
again  fall,  or  whether  it  would  have  fallen  had  i 
been  taken  up  an  hour  sooner.  This  experiment 
alone  gives  him  no  light  respecting  these  particu- 
lars. 

The  man  in  question  takes  another  stone,  ana 
observes  that  it  falls  likewise,  whether  dropped  from 
the  right  hand  or  from  the  left :  he  repeats  the  ex- 
periment with  a  third  and  a  fourth  stone,  and  uni- 
formly observes  the  same  effect.  He  hence  con- 
cludes that  stones  have  the  property  of  falling  when 
dropped,  or  when  that  which  supports  them  is  with- 
drawn. 

Here  then  is  an  article  of  knowledge  which  the 
man  has  derived  from  the  experiments  which  he  has 
made.  He  is  very  far  from  having  made  trial  of 
every  stone,  or,  supposing  him  to  have  done  so, 
what  certainty  has  he  that  the  same  thing  would 
happen  at  all  times  T  He  knows  nothing  as  to  this, 
except  what  concerns  the  particular  moments  when 
he  made  the  experiments ;  and  what  assurance  has 
he  that  the  same  effect  would  take  place  in  the 
hands  of  another  man?  Might  he  not  think  that 
this  quality  of  making  stones  fall  was  attached  to 
his  hands  exclusively  ^  A  thousand  other  doubts 
might  still  be  formed  on  the  subject. 

I  have  never,  for  example,  made  trial  of  the  stones 
which  compose  the  cathedral  church  of  Magdeburg, 
and  yet  I  have  not  the  least  doubt  that  all  of  them, 
without  exception,  are  heavy,  and  that  each  of  them 
would  fall  as  soon  as  detached  from  the  building. 
I  even  imagine  that  experience  has  supplied  me  with 
this  knowledge,  though  I  have  never  tried  any  one 
of  those  stones. 


THE    INCREASE    OF    KNOWLEDGE.  25 

This  example  is  sufficient  to  show  how  experi- 
ments made  on  individual  objects  only  have  led 
mankind  to  the  knowledge  of  universal  propositions; 
but  it  must  be  admitted  that  the  understanding  and 
the  other  faculties  of  the  soul  interfere  in  a  manner 
which  it  would  be  extremely  difficult  clearly  to  un- 
fold ;  and  if  we  were  determined  to  be  over-scrupu- 
lous about  every  circumstance,  no  progress  in  sci- 
ence could  be  made,  for  we  should  be  stopped  short 
at  every  step. 

It  must  be  allowed,  that  the  vulgar  discover  in 
this  respect  much  more  good  sense  than  those  scru- 
pulous philosophers  who  are  obstinately  determined 
to  doubt  of  every  thing.  It  is  necessary,  at  the  same 
time,  to  be  on  our  guard  against  falling  into  the 
opposite  extreme,  by  neglecting  to  employ  the 
necessary  precautions. 

The  three  sources  from  which  our  knowledge  is 
derived  require  all  of  them  certain  precautions, 
which  must  be  carefully  observed,  in  order  to  ac- 
quire assurance  of  the  truth ;  but  it  is  possible,  in 
each,  to  carry  matters  too  far,  and  it  is  always  proper 
to  steer  a  middle  course. 

The  third  source  clearly  proves  this.  It  would 
undoubtedly  be  extreme  folly  to  believe  every  thing 
that  is  told  us ;  but  excessive  distrust  would  be  no 
less  blameworthy.  He  who  is  determined  to  doubt 
of  every  thing  will  never  want  a  pretence ;  when  a 
man  says  or  writes  that  he  has  seen  such  or  such 
an  action,  we  may  say  at  once  that  it  is  not  true,  and 
that  the  man  takes  amusement  in  relating  things 
which  may  excite  surprise ;  and  if  his  veracity  is 
beyond  suspicion,  it  might  be  said  that  he  did  not 
see  clearly,  that  his  eyes  were  dazzled  ;  and  exam- 
ples are  to  be  found  in  abundance  of  persons  deceiv- 
ing themselves,  falsely  imagining  they  saw  what 
they  did  not.  The  rules  prescribed  in  this  respect 
lose  all  their  weight  when  you  have  to  do  with  a 
wrangler. 

VOL  II.— C 


26  WHETHER    THE    ESSENCE    OF 

Usually,  in  order  to  be  ascertained  of  the  truth  of 
a  recital  or  history,  it  is  required  that  the  author 
should  have  been  himself  a  witness  of  what  he  re- 
lates, and  that  he  should  have  no  interest  in  relating 
it  differently  from  the  truth.  If  afterward  two  or 
more  persons  relate  the  same  thing,  with  the  same 
circumstances,  it  is  justly  considered  as  a  strong 
confirmation.  Sometimes,  however,  a  coincidence 
carried  to  extreme  minuteness  becomes  suspicious. 
For  two  persons  observing  the  same  incident  see  it 
in  different  points  of  view ;  and  the  one  will  always 
discern  certain  little  circumstances  which  the  other 
must  have  overlooked.  A  slight  difference  in  two 
several  accounts  of  the  same  event  rather  estab- 
lishes than  invalidates  the  truth  of  it. 

But  it  is  always  extremely  difficult  to  reason  on 
the  first  principles  of  our  knowledge,  and  to  attempt 
an  explanation  of  the  mechanism  and  of  the  moving 
powers  which  the  soul  employs.  It  would  be  glo- 
rious to  succeed  in  such  an  attempt,  as  it  would 
elucidate  a  great  variety  of  important  points  respect- 
ing the  nature  of  the  soul  and  its  operations.  But 
we  seem  destined  rather  to  make  use  of  our  facul- 
ties, than  to  trace  their  nature  through  all  its  depths. 

18th  April,  1761. 


LETTER  VI. 

Whether  the  Essence  of  Bodies  be  known  by  us. 

AFTER  so  many  reflections  on  the  nature  and 
faculties  of  the  soul,  you  will  not  perhaps  be  dis- 
pleased to  return  to  the  consideration  of  body,  the 
principal  properties  of  which  I  have  already  en- 
deavoured to  explain. 

I  have  remarked,  that  the  nature  of  body  neces- 
sarily contains  three  things,  extension,  impenetrability, 
and  inertia ;  so  that  a  being  in  which  these  three  prop- 


BODIES    BE    KNOWN   BY    US.  27 

erties  do  not  meet  at  once  cannot  be  admitted  into 
the  class  of  bodies  ;  and  reciprocally,  when  they  are 
united  in  any  one  being,  no  one  will  hesitate  to  ac- 
knowledge it  for  a  body. 

In  these  three  things,  then,  we  are  warranted  to 
constitute  the  essence  of  body,  though  there  are 
many  philosophers  who  pretend  that  the  essence  of 
bodies  is  wholly  unknown  to  us.  This  is  not  only 
the  opinion  of  the  Pyrrhonists,  who  doubt  of  every 
thing ;  but  there  are  other  sects  likewise  who  main- 
tain that  the  essence  of  all  things  is  absolutely  un- 
known :  and,  no  doubt,  in  certain  respects  they  have 
truth  on  their  side :  this  is  but  too  certain  as  to  all 
the  individual  beings  which  exist. 

You  will  easily  comprehend,  that  it  would  be  the 
height  of  absurdity  were  I  to  pretend  so  much  as  to 
know  the  essence  of  the  pen  which  I  employ  in 
writing  this  Letter.  If  I  knew  the  essence  of  this 
pen  (I  speak  not  of  pens  in  general,  but  of  that  one 
only  now  between  my  fingers,  which  is  an  individual 
'being,  as  it  is  called  in  metaphysics,  and  which  is 
distinguished  from  all  the  other  pens  in  the  world), 
if  I  knew,  then,' the  essence  of  this  individual  pen,  I 
should  be  in  a  condition  to  distinguish  it  from  every 
other,  and  it  would  be  impossible  to  change  it  with- 
out my  perceiving  the  change;  I  must  know  its 
nature  thoroughly,  the  number  and  the  arrangement 
of  all  the  parts  whereof  it  is  composed.  But  how 
far  am  I  from  having  such  a  knowledge  !  Were  I  to 
rise  but  for  a  moment,  one  of  my  children  might 
easily  change  it,  leaving  another  in  its  room,  with- 
out my  perceiving  the  difference  ;  and  were  I  even 
to  put  a  mark  upon  it,  how  easily  might  that  mark 
be  counterfeited  on  another  pen.  And  supposing 
this  impossible  for  my  children,  it  must,  always  be 
admitted  as  possible  for  God  to  make  another  pen 
so  similar  to  this  that  I  should  be  unable  to  discern 
any  difference.  It  would  be,  however,  another  pen, 
really  distinguishable  from  mine,  and  God  would 


28  WHETHER   THE    ESSENCE    OF 

undoubtedly  know  the  difference  of  them ;  in  other 
words,  God  perfectly  knows  the  essence  of  both 
the  one  and  the  other  of  these  two  pens :  but  as  to 
me,  who  discern  no  difference,  it  is  certain  that  the 
essence  is  altogether  beyond  my  knowledge. 

The  same  observation  is  applicable  to  all  other 
individual  things ;  and  it  may  be  confidently  main- 
tained, that  God  alone  can  know  the  essence  or 
nature  of  each.  It  were  impossible  to  fix  on  any 
one  thing  really  existing  of  which  we  could  have  a 
knowledge  so  perfect  as  to  put  us  beyond  the  reach 
of  mistake :  this  is,  if  I  may  use  the  expression,  the 
impress  of  the  Creator  on  all  created  things,  the 
nature  of  which  will  ever  remain  a  mystery  to  us. 

It  is  undoubtedly  certain,  then,  that  we  do  not 
know  the  essence  of  individual  things,  or  all  the 
characters  whereby  each  is  distinguished  from  every 
other ;  but  the  case  is  different  with  respect  to 
genera  and  species :  these  are  general  notions  which 
include  at  once  an  infinite  number  of  individual 
things.  They  are  not  beings  actually  existing,  but 
notions  which  we  ourselves  form  in  our  minds  when 
we  arrange  a  great  many  individual  things  in  the 
same  class,  which  we  denominate  a  species  or 
genus,  according  as  the  number  of  individual  things 
which  it  comprehends  is  greater  or  less. 

And  to  return  to  the  example  of  the  pen,  as  there 
are  an  infinite  number  of  things  to  each  of  which  I 
give  the  same  name,  though  they  all  differ  one  from 
another,  the  notion  of  pen  is  a  general  idea,  of  which 
we  ourselves  are  the  creators,  and  which  exists 
only  in  our  own  minds.  This  notion  contains  but 
the  common  characters  which  constitute  the  essence 
of  the  general  notion  of  a  pen ;  and  this  essence 
must  be  well  known  to  us,  as  we  are  in  a  condition 
to  distinguish  all  the  things  which  we  call  pens 
from  those  which  we  do  not  comprehend  under  that 
appellation. 

As  soon  as  we  remark  in  any  thing  certain  char 


BODIES    BE    KNOWN   BY    US.  29 

acters,  or  certain  qualities,  we  say  it  is  a  pen ;  and 
we  are  in  a  condition  to  distinguish  it  from  all  other 
things  which  are  not  pens,  though  we  are  very  far 
from  being  able  to  distinguish  it  from  other  pens. 

The  more  general  a  notion  is,  the  fewer  it  contains 
of  the  characters  which  constitute  its  essence ;  and 
it  is  accordingly  easier  also  to  discover  this  essence. 
We  comprehend  more  easily  what  is  meant  by  a 
tree  in  general  than  by  the  term  cherry-tree,  pear- 
tree,  or  apple-tree ;  that  is,  when  we  descend  to  the 
species.  When  I  say  such  an  object  which  I  see  in 
the  garden  is  a  tree,  I  run  little  risk  of  being  mis- 
taken; but  it  is  extremely  possible  I  might  be  wrong 
if  I  affirmed  it  was  a  cherry-tree.  It  follows,  then, 
that  I  know  much  better  the  essence  of  tree  in 
general  than  of  the  species ;  I  should  not  so  easily 
confound  a  tree  with  a  stone  as  a  cherry-tree  with 
a  plum-tree. 

Now  a  notion  in  general  extends  infinitely  fur- 
ther; its  essence  accordingly  comprehends  only 
the  characters  which  are  common  to  all  beings  bear- 
ing the  name  of  bodies.  It  is  reduced,  therefore,  to 
a  very  few  particulars,  as  we  must  exclude  from  it 
all  the  characters  which  distinguish  one  body  from 
another. 

It  is  ridiculous,  then,  to  pretend  with  certain  phi- 
losophers that  the  essence  of  bodies  in  general  is 
unknown  to  us.  If  it  were  so,  we  should  never  be 
in  a  condition  to  affirm  with  assurance  that  such  a 
thing  is  a  body,  or  it  is  not ;  and  as  it  is  impossible 
we  should  be  mistaken  in  this  respect,  it  necessarily 
follows  that  we  know  sufficiently  the  nature  or  es- 
sence of  body  in  general.  Now  this  knowledge  is 
reduced  to  three  articles :  extension,  impenetrability, 
and  inertia. 

21st  April,  1761. 

C2 


30  TRUE   NOTION    OF   EXTENSION. 

LETTER  VII. 

The  True  Notion  of  Extension. 

I  HAVE  already  demonstrated  that  the  general 
notion  of  body  necessarily  comprehends  these  three 
qualities,  exterasion,  impenetrability,  and  inertia, 
without  which  no  being  can  be  ranked  in  the  class 
of  bodies.  Even  the  most  scrupulous  must  allow 
the  necessity  of  these  three  qualities  in  order  to 
constitute  a  body ;  but  the  doubt  with  some  is,  Are 
these  three  characters  sufficient?  Perhaps,  say 
they,  there  may  be  several  other  characters  which 
are  equally  necessary  to  the  essence  of  body. 

But  I  ask,  were  God  to  create  a  being  divested  of 
these  other  unknown  characters,  and  that  it  pos- 
sessed only  the  three  above  mentioned,  would  they 
hesitate  to  give  the  name  of  body  to  such  a  being  ? 
No,  assuredly ;  for  if  they  had  the  least  doubt  on  the 
subject,  they  could  not  say  with  certainty  that  the 
stones  in  the  street  are  bodies,  because  they  are  not 
sure  whether  the  pretended  unknown  characters  are 
to  be  found  in  them  or  not. 

Some  imagine  that  gravity  is  an  essential  property 
of  all  bodies,  as  all  those  which  we  know  are  heavy; 
but  were  God  to  divest  them  of  gravity,  would  they 
therefore  cease  to  be  bodies  1  Let  them  consider 
the  heavenly  bodies,  which  do  not  fall  downward ; 
as  must  be  the  case  if  they  were  heavy  as  the  bodies 
which  we  touch,  yet  they  give  them  the  same  name. 
And  even  on  the  supposition  that  all  bodies  were 
heavy,  it  would  not  follow  that  gravity  is  a  property 
essential  to  them,  for  a  body  would  still  remain  a 
body,  though  its  gravity  were  to  be  destroyed  by  a 
miracle. 

But  this  reasoning  does  not  apply  to  the  three  es- 
sential properties  above  mentioned.  Were  God  to 


TRUE  NOTION  OF  EXTENSION.        31 

annihilate  the  extension  of  a  body,  it  would  cer- 
tainly be  no  longer  a  body;  and  a  body  divested 
of  impenetrability  would  no  longer  be  lody ;  it 
would  be  a  spectre,  a  phantom  :  the  same  holds  as 
to  inertia. 

You  know  that  extension  is  the  proper  object  of 
geometry,  which  considers  bodies  only  in  so  far  as 
they  are  extended,  abstractedly  from  impenetrability 
and  inertia ;  the  object  of  geometry,  therefore,  is  a 
notion  much  more  general  than  that  of  body,  as  it 
comprehends,  not  only  bodies,  but  all  things  simply 
extended,  without  impenetrability,  if  any  such  there 
be.  Hence  it  follows  that  all  the  properties  deduced 
In  geometry  from  the  notion  of  extension  must  like- 
wise take  place  in  bodies,  inasmuch  as  they  are  ex- 
tended ;  for  whatever  is  applicable  to  a  more  general 
notion,  to  that  of  a  tree,  for  example,  must  likewise 
be  applicable  to  the  notion  of  an  oak,  an  ash,  an 
elm,  &c. ;  and  this  principle  is  even  the  foundation 
of  all  the  reasonings  in  virtue  of  which  we  always 
affirm  and  deny  of  the  species,  and  of  individuals, 
every  thing  that  we  affirm  and  deny  of  the  genus. 

There  are  however  philosophers,  particularly 
among  our  contemporaries,  who  boldly  deny  that 
the  properties  applicable  to  extension  in  general, 
that  is,  according  as  we  consider  them  in  geometry, 
take  place  in  bodies  really  existing.  They  allege 
that  geometrical  extension  is  an  abstract  being,  from 
the  properties  of  which  it  is  impossible  to  draw  any 
conclusion  with  respect  to  real  objects  ;  thus,  when 
I  have  demonstrated  that  the  three  angles  of  a  tri- 
angle are  together  equal  to  two  right  anglesj  this  is 
a  property  belonging  only  to  an  abstract  triangle, 
and  not  at  all  to  one  really  existing. 

But  these  philosophers  are  not  aware  of  the  per- 
plexing consequences  which  naturally  result  from 
the  difference  which  they  establish  between  objects 
formed  by  abstraction  and  real  objects ;  and  if  it 
were  not  permitted  to  conclude  frota  the  first  to  the 


32  TRUE    NOTION    OF    EXTENSION. 

last,  no  conclusion,  and  no  reasoning  whatever, 
could  subsist,  as  we  always  conclude  from  general 
notions  to  particular. 

Now  all  general  notions  are  as  much  abstract 
beings  as  geometrical  extension;  and  a  tree  in 
general,  or  the  general  notion  of  trees,  is  formed 
only  by  abstraction,  and  no  more  exists  out  of  our 
mind  than  geometrical  extension  does.  The  notion 
of  man  in  general  is  of  the  same  kind,  and  man  in 
general  nowhere  exists  :  all  men  who  exist  are  in- 
dividual beings,  and  correspond  to  individual  notions. 
The  general  idea  which  comprehends  all  is  formed 
only  by  abstraction. 

The  fault  which  these  philosophers  are  ever  find- 
ing with  geometricians,  for  employing  themselves 
about  abstractions  merely,  is  therefore  groundless, 
as  all  other  sciences  principally  turn  on  general  no- 
tions, which  are  no  more  real  than  the  objects  of 
geometry.  The  patient,  in  general,  whom  the  phy- 
sician has  in  view,  and  the  idea  of  whom  contains 
all  patients  really  existing,  is  only  an  abstract  idea ; 
nay,  the  very  merit  of  each  science  is  so  much  the 
greater,  as  it  extends  to  notions  more  general,  that 
is  to  say,  more  abstract. 

I  shall  endeavour  by  next  post  to  point  out  me 
tendency  of  the  censures  pronounced  by  these  phi- 
losophers upon  geometricians  ;  and  the  reasons  why 
they  are  unwilling  that  we  should  ascribe  to  real  ex- 
tended beings,  that  is,  t.o  existing  bodies,  the  proper- 
ties applicable  to  extension  in  general,  or  to  ab- 
stracted extension.  They  are  afraid  lest  their  meta- 
physical principles  should  suffer  in  the  cause. 

25th  April,  1761. 


DIVISIBILITY    OF    EXTENSION. 


33 


LETTER  VIII. 

Divisibility  of  Extension  in  infinitum. 

THE  controversy  between  modern  philosophers 
and  geometricians,  to  which  I  have  alluded,  turns  on 
the  divisibility  of  body.  This  property  is  undoubt- 
edly founded  on  extension ;  and  it  is  only  in  so  far 
as  bodies  are  extended  that  they  are  divisible,  and 
capable  of  being  reduced  to  parts. 

You  will  recollect  that  Fig.  38. 

in  geometry  it  is  always  A  B    c    D    E    F    <J_H I 

possible  to  divide  a  line, 
however  small,  into  two 
equal  parts.  We  are 
likewise  by  that  science 
instructed  in  the  method 
of  dividing  a  small  line, 
as  a  i,  Fig.  38,  into  any 
number  of  equal  parts  at 
pleasure:  and  the  con- 
struction of  this  division 
is  there  demonstrated 
beyond  the  possibility  of 
doubting  its  accuracy. 

You  have  only  to  draw 
a  line  A  I  parallel  to  a  i 
of  any  length,  and  at  any 
distance  you  please,  and 
to  divide  it  into  as  many 
equal  parts  AB,  BC,  CD,  o 
DE,  &c.  as  the  small 

line  given  is  to  have  divisions,  say  eight.  Draw 
afterward,  through  the  extremities  A  a,  and  I  i,  the 
straight  lines  A  a  0, 1  i  O,  till  they  meet  in  the  point 
O ;  and  from  0  draw  towards  the  points  of  division 
B,  C,  D,  E,  &c.  the  straight  lines  OB,  OC,  OD,  OE, 


34  DIVISIBILITY   o* 

&c.,  which  shall  likewise  divide  the  small  line  a  i 
into  eight  equal  parts. 

This  operation  may  be  performed,  however  small 
the  given  line  a  i,  and  however  great  the  number  of 
parts  into  which  you  propose  to  divide  it.  It  is  true 
that  in  execution  we  are  not  permitted  to  go  too 
far ;  the  lines  which  we  draw  have  always  some 
breadth,  whereby  they  are  at  length  confounded,  as 
may  be  seen  in  the  figure  near  the  point  O  ;  but  the 
question  is,  not  what  may  be  possible  for  us  to  exe- 
cute, but  what  is  possible  in  itself.  Now,  in  geome- 
try lines  have  no  breadth,  and  consequently  can 
never  be  confounded.  Hence  it  follows  that  such 
division  is  illimitable. 

If  it  is  once  admitted  that  a  line  may  be  divided 
into  a  thousand  parts,  by  dividing  each  part  into  two 
it  will  be  divisible  into  two  thousand  parts,  and  for 
the  same  reason  into  four  thousand,  and  into  eight 
thousand,  without  ever  arriving  at  parts  indivisible. 
However  small  a  line  may  be  supposed,  it  is  still 
divisible  into  halves,  and  each  half  again  into  two, 
and  each  of  these  again  in  like  manner,  and  so  on 
to  infinity. 

What  I  have  said  of  a  line  is  easily  applicable  to 
a  surface,  and,  with  greater  strength  of  reasoning, 
to  a  solid  endowed  with  three  dimensions,— length, 
breadth,  and  thickness.  Hence  it  is  affirmed  that  all 
extension  is  divisible  to  infinity  ;  and  this  property  is 
denominated  divisibility  in  infinilum. 

Whoever  is  disposed  to  deny  this  property  of  ex- 
tension is  under  the  necessity  of  maintaining  that  it 
is  possible  to  arrive  at  last  at  parts  so  minute  as  to 
be  unsusceptible  of  any  further  division,  because 
they  cease  to  have  any  extension.  Nevertheless, 
all  these  particles  taken  together  must  reproduce  the 
whole,  by  the  division  of  which  you  acquired  them ; 
and  as  the  quantity  of  each  would  be  a  nothing  or 
cipher  0,  a  combination  of  ciphers  would  produce 
quantity,  which  is  manifestly  absurd.  For  you  know 


EXTENSION   IN   INFINITUM.  35 

perfectly  well  that  in  arithmetic  two  or  more  ciphers 
joined  never  produce  any  thing-. 

This  opinion,  that  in  the  division  of  extension  or 
of  any  quantity  whatever,  we  may  come  at  last  to 
particles  so  minute  as  to  be  no  longer  divisible, 
because  they  are  so  small,  or  because  quantity  no 
longer  exists,  is  therefore  a  position  absolutely  un- 
tenable. 

In  order  to  render  the  absurdity  of  it  more  sensi- 
ble, let  us  suppose  a  line  of  an  inch  long  divided  into 
a  thousand  parts,  and  that  these  parts  are  so  small 
as  to  admit  of  no  further  division ;  each  part,  then, 
would  no  longer  have  any  length,  for  if  it  had  any  it 
would  be  still  divisible.  Each  particle,  then,  would 
of  consequence  be  a  nothing.  But  if  these  thou- 
sand particles  together  constituted  the  length  of  an 
inch,  the  thousandth  part  of  an  inch  would  of  con- 
sequence be  a  nothing  ;  which  is  equally  absurd  with 
maintaining  that  the  half  of  any  quantity  whatever 
is  nothing.  And  if  it  be  absurd  to  affirm  that  the 
half  of  any  quantity  is  nothing,  it  is  equally  so  to 
affirm  that  the  half  of  a  half,  or  that  the  fourth  part 
of  the  same  quantity  is  nothing ;  and  what  must  be 
granted  as  to  the  fourth  must  likewise  be  granted 
with  respect  to  the  thousandth  and  the  millionth 
part.  Finally,  however  far  you  may  have  already 
carried  in  imagination  the  division  of  an  inch,  it  is 
always  possible  to  carry  it  still  further ;  and  never 
will  you  be  able  to  carry  on  your  subdivision  so  far 
as  that  the  last  parts  shall  be  absolutely  indivisible. 
These  parts  will  undoubtedly  always  become  smaller, 
and  their  magnitude  will  approach  nearer  and  nearer 
to  0,  but  can  never  reach  it. 

The  geometrician,  therefore,  is  warranted  in  af- 
firming that  every  magnitude  is  divisible  to  infinity; 
and  that  you  cannot  proceed  so  far  in  your  division 
as  that  all  further  division  shall  be  impossible.  But 
it  is  always  necessary  to  distinguish  between  what 
is  possible  in  itself  and  what  we  are  in  a  condition 


36  WHETHER   THIS    DIVISIBILITY    TAKES 

to  perform.  Our  execution  is  indeed  extremely 
limited.  After  having,  for  example,  divided  an  inch 
into  a  thousand  parts,  these  parts  are  so  small  as  to 
escape  our  senses  -r  and  a  further  division  would  to 
us  no  doubt  be  impossible. 

But  you  have  only  to  look  at  this  thousandth  part 
of  an  inch  through  a  good  microscope,  which  mag- 
nifies, for  example,  a  thousand  times,  and  each  par- 
ticle will  appear  as  large  as  an  inch  to  the  naked 
eye ;  and  you  will  be  convinced  of  the  possibility 
of  dividing  each  of  these  particles  again  into  a  thou- 
sand parts :  the  same  reasoning  may  always  be  car- 
ried forward  without  limit  and  without  end. 

It  is  therefore  an  indubitable  truth  that  all  magni- 
tude is  divisible  in  infinitum ;  and  that  this  takes  place 
not  only  with  respect  to  extension,  which  is  the 
object  of  geometry,  but  likewise  with  respect  to 
every  other  species  of  quantity,  such  as  time  and 
number. 

28th  April,  1761. 

LETTER  IX. 

Whether  this  Divisibility  in  infinitum  takes  place  in  ex- 
isting Bodies. 

It  is  then  a  completely  established  truth,  that  ex- 
tension is  divisible  to  infinity,  and  that  it  is  impossi- 
ble to  conceive  parts  so  small  as  to  be  unsusceptible 
of  further  division.  Philosophers  accordingly  do  not 
impugn  this  truth  itself,  but  deny  that  it  takes  place 
in  existing  bodies.  They  allege  that  extension,  the 
divisibility  of  which  to  infinity  has  been  demon- 
strated, is  merely  a  chimerical  object,  formed  by  ab- 
straction ;  and  that  simple  extension,  as  considered 
in  geometry,  can  have  no  real  existence. 

Here  they  are  in  the  right ;  and  extension  is  un- 
doubtedly a  general  idea,  formed  in  the  same  man- 


PLACE    IN   EXISTING   BODIES.  37 

tier  as  that  of  man,  or  of  tree  in  general,  by  ab- 
straction ;  and  as  man  or  tree  in  general  does  not 
exist,  no  more  does  extension  in  general  exist.  You 
are  perfectly  sensible  that  individual  beings  alone 
exist,  and  that  general  notions  are  to  be  found  only 
in  the  mind ;  but  it  cannot  therefore  be  maintained 
that  these  general  notions  are  chimerical ;  they 
contain,  on  the  contrary,  the  foundation  of  all  our 
knowledge. 

Whatever  applies  to  a  general  notion,  and  all  the 
properties  attached  to  it,  of  necessity  takes  place  in 
all  the  individuals  comprehended  under  that  general 
notion.  When  it  is  affirmed  that  the  general  no- 
tion of  man  contains  an  understanding  and  a  will,  it 
is  undoubtedly  meant  that  every  individual  man  is 
endowed  with  those  faculties.  And  how  many  prop- 
erties do  these  very  philosophers  boast  of  having 
demonstrated  as  belonging  to  substance  in  general, 
which  is  surely  an  idea  as  abstract  as  that  of  exten- 
sion ;  and  yet  they  maintain  that  all  these  proper- 
ties apply  to  all  individual  substances,  which  are  all 
extended.  If,  in  effect,  such  a  substance  had  not 
these  properties,  it  would  be  false  that  they  belonged 
to  substance  in  general. 

If  then  bodies,  which  infallibly  are  extended  be- 
ings, or  endowed  with  extension,  were  not  divisible 
to  infinity,  it  would  be  likewise  false  that  divisibility 
in  infinitum  is  a  property  of  extension.  Now  those 
philosophers  readily  admit  that  this  property  belongs 
to  extension,  but  they  insist  that  it  cannot  take  place 
in  extended  beings.  This  is  the  same  thing  with 
affirming  that  the  understanding  and  will  are  indeed 
attributes  of  the  notion  of  man  in  general,  but  that 
they  can  have  no  place  in  individual  men  actually 
existing. 

Hence  you  will  readily  draw  this  conclusion  :  If 
divisibility  in  infinitum  is  a  property  of  extension  in 
general,  it  must  of  necessity  likewise  belong  to  all 
individual  extended,  beings;  or  if  real  extended 

VOL.  II.— D 


38  DIVISIBILITY    OF    EXISTING    BODIES. 

beino-s  are  not  divisible  to  infinity,  it  is  false  that  divi- 
sibility in  infinitura  can  be  a  property  of  extension 
in  general.  ,, 

It  is  impossible  to  deny  the  one  or  the  other  o 
these  consequences  without  subverting  the  must 
solid  principles  of  all  knowledge ;  and  the  philoso- 
phers who  refuse  to  admit  divisibility  m  infimtum  m 
real  extended  beings  ought  as  little  to  admit  it  with 
respect  to  extension  in  general ;  but  as  they  grant 
this  last,  they  fall  into  a  glaring  contradiction. 

You  need  not  be  surprised  at  this ;  it  is  a  failing 
from  which  the  greatest  men  are  not  exempt.  But 
what  is  rather  surprising,  these  philosophers,  m 
order  to  get  rid  of  their  embarrassment,  have  thought 
proper  to  deny  that  body  is  extended.  They  say, 
that  it  is  only  an  appearance  of  extension  which  is 
perceived  in  bodies,  but  that  real  extension  by  no 
means  belongs  to  them. 

You  see  clearly  that  this  is  merely  a  wretched 
cavil  bv  which  the  principal  and  the  most  evident 
property  of  body  is  denied.     It  is  an  extravagance 
similar  to  that  formerly  imputed  to  the  Epicurean 
philosophers,  who  maintained  that  every  thing  which 
exists  in  the  universe  is  material,  without  even  ex- 
cepting the  gods,  whose  existence  they  admitted. 
But  as  they  saw  that  these  corporeal  gods  would  be 
subjected  to  the  greatest  difficulties,  they  invented 
a  subterfuge  similar  to  that  of  our  modern  philoso- 
phers, alleging,  that  the  gods  had  not  bodies .but  as 
it  were  bodies  (quasi  corpora),  and  that  they  had  not 
senses,  but  senses  as  it  were ;    and  so  ol  all  me 
members.     The  other  philosophical  sects  oi  anti- 
quity made  themselves  abundantly  merry  with  these 
quasi  corpora  and  quasi  sensus ;  and  they  would  have 
equal  reason  in  modern  times  to  laugh  at  the •.quasi 
extension  which  our  philosophers  ascribe  to  body  ; 
this  term  quasi  extension  seems  perfectly  well  to  ex- 
press that  appearance  of  extension,  without  being  so 
in  reality. 


OF    MONADS.  39 

Geometricians,  if  they  meant  to  confound  them, 
have  only  to  say  that  the  objects  whose  divisibility 
in  infinitum  they  have  demonstrated  were  likewise 
only  as  it  were  extended,  and  that  accordingly  all 
bodies  extended  as  it  were  were  necessarily  divisible 
in  infinitum.  But  nothing  is  to  be  gained  with  them  ; 
they  resolve  to  maintain  the  greatest  absurdities 
rather  than  acknowledge  a  mistake. 

3d  May,  1761. 


LETTER  X. 

Of  Monads. 

WHEN  we  talk  in  company  on  philosophical  sub 
iects,  the  conversation  usually  turns  on  such  arti 
cles  as  have  excited  violent  disputes  among  philoso- 
phers. 

The  divisibility  of  body  is  one  of  them,  respecting 
which  the  sentiments  of  the  learned  are  greatly 
divided.  Some  maintain  that  this  divisibility  goes 
on  to  infinity,  without  the  possibility  of  ever  arriving 
at  particles  so  small  as  to  be  susceptible  of  no  fur- 
ther division.  But  others  insist  that  this  division 
extends  only  to  a  certain  point,  and  that  you  may 
come  at  length  to  particles  so  minute  that,  having 
no  magnitude,  they  are  no  longer  divisible.  These 
ultimate  particles,  which  enter  into  the  composi 
tion  of  bodies,  they  denominate  simple  beings  and 
monads. 

There  was  a  time  when  the  dispute  respecting 
monads  employed  such  general  attention,  and  was 
conducted  with  so  much  warmth,  that  it  forced  its 
way  into  company  of  every  description,  that  of  the 
guard-room  not  excepted.  There  was  scarcely  a 
lady  at  court  who  did  not  take  a  decided  part  in  fa- 
vour of  monads  or  against  them.  In  a  word,  all  con- 


40  OF    MONADS. 

versation  was  engrossed  by  monads — no  other  sub- 
ject could  find  admission. 

The  Royal  Academy  of  Berlin  took  up  the  con- 
troversy, and  being  accustomed  annually  to  propose 
a  question  for  discussion,  and  to  bestow  a  gold  medal, 
of  the  value  of  fifty  ducats,  on  the  person  who,  in 
the  judgment  of  the  Academy,  has  given  the  most 
ino-enious  solution,  the  question  respecting  monads 
was  selected  for  the  year  1748.  A  great  variety  of 
essays  on  the  subject  were  accordingly  produced. 
The  president,  Mr.  de  Maupertuis,  named  a  com- 
mittee to  examine  them,  under  the  direction  of  the 
late  Count  Dohna,  great  chamberlain  to  the  queen ; 
who,  being  an  impartial  judge,  examined  with  all 
imaginable  attention  the  arguments  adduced  both 
for  and  against  the  existence  of  monads.  Upon  the 
whole,  it  was  found  that  those  which  went  to  the 
establishment  of  their  existence  were  so  feeble  and 
so  chimerical,  that  they  tended  to  the  subversion  of 
all  the  principles  of  human  knowledge.  The  question 
was  therefore  determined  in  favour  of  the  opposite 
opinion,  and  the  prize  adjudged  to  Mr,  Justi,  whose 
piece  was  deemed  the  most  complete  refutation  of 
the  monad  ists. 

You  may  easily  imagine  how  violently  this  de- 
cision of  the  Academy  must  have  irritated  the  parti- 
sans of  monads,  at.  the  head  of  whom  stood  the  cele- 
brated Mr.  Wolff.  His  followers,  who  were  then  much 
more  numerous  and  more  formidable  than  at  pres- 
ent, exclaimed  in  high  terms  against  the  partiality 
and  injustice  of  the  Academy  ;  and  their  chief  had 
vvellnigh  proceeded  to  launch  the  thunder  of  a  phi- 
losophical anathema  against  it.  1  do  not  now  recol- 
lect to  whom  we  are  indebted  for  the  care  of  avert- 
ing this  disaster. 

As  this  controversy  has  made  a  great  deal  of  noise, 
you  will  not  be  displeased,  undoubtedly,  if  I  dwell  a 
little  upon  it.  The  whole  is  reduced  to  this  simple 
question,  Is  body  divisible  to  infinity  ?  or,  in  other 


OF    MONADS.  41 

words,  Has  the  divisibility  of  bodies  any  bound,  or 
has  it  not  1  I  have  already  remarked  as  to  this,  that 
extension,  geometrically  considered,  is  on  all  hands 
allowed  to  be  divisible  in  infmitum ;  because  how- 
ever small  a  magnitude  may  be,  it  is  possible  to  con- 
ceive the  half  of  it,  and  again  the  half  of  that  half, 
and  so  on  to  infinity. 

This  notion  of  extension  is  very  abstract,  as  are 
those  of  all  genera,  such  as  that  of  man,  of  horse,  of 
tree,  £c.,  as  far  as  they  are  not  applied  to  an  indi- 
vidual and  determinate  being.  Again,  it  is  the  most 
certain  principle  of  all  our  knowledge,  that  whatever 
can  be  truly  affirmed  of  the  genus  must  be  true  of 
all  the  individuals  comprehended  under  it.  If  there- 
fore all  bodies  are  extended,  all  the  properties  be- 
longing to  extension  must  belong  to  each  body  in 
particular.  Now  all  bodies  are  extended,  and  ex- 
tension is  divisible  to  infinity;  therefore  every  body 
must  be  so  likewise.  This  is  a  syllogism  of  the 
best  form ;  and  as  the  first  proposition  is  indubitable, 
all  that  remains  is  to  be  assured  that  the  second  is 
true,  that  is,  whether  it  be  true  or  not  that  bodies 
are  extended. 

The  partisans  of  monads,  in  maintaining  theif 
opinion,  are  obliged  to  affirm  that  bodies  are  not  ex- 
tended, but  have  only  an  appearance  of  extension. 
They  imagine  that  by  this  they  have  subverted  the 
argument  adduced  in  support  of  the  divisibility  in 
infinitum.  But  if  body  is  not  extended,  I  should  be 
glad  to  know  from  whence  we  derived  the  idea  of 
extension ;  for  if  body  is  not  extended,  nothing  in 
the  world  is,  as  spirits  are  still  less  so.  Our  idea  of 
extension,  therefore,  would  be  altogether  imaginary 
and  chimerical. 

Geometry  would  accordingly  be  a  speculation  en- 
tirely useless  and  illusory,  and  never  could  admit  of 
any  application  to  things  really  existing.  In  effect, 
if  no  one  thing  is  extended,  to  "what  purpose  investi- 
gate the  properties  of  extension  ?  But  as  geometry 
D2 


42  REFLECTIONS    ON   DIVISIBILITY, 

is  beyond  contradiction  one  of  the  most  useful  of 
the  sciences,  its  object  cannot  possibly  be  a  mere 
chimera. 

There  is  a  necessity  then  of  admitting,  that  the 
object  of  geometry  is  at  least  the  same  apparent  ex- 
tension which  those  philosophers  allow  to  body ;  but 
this  very  object  is  divisible  to  infinity :  therefore  ex- 
isting beings  endowed  with  this  apparent  extension 
must  necessarily  be  extended. 

Finally,  let  those  philosophers  turn  themselves 
which  way  soever  they  will  in  support  of  their  mo- 
nads, or  those  ultimate  and  minute  particles  divested 
of  all  magnitude,  of  which,  according  to  them,  all 
bodies  are  composed,  they  still  plunge  into  difficul- 
ties, out  of  which  they  cannot  extricate  themselves. 
They  are  right  in  saying  that  it  is  a  proof  of  dul- 
ness  to  be  incapable  of  relishing  their  sublime  doc- 
trine ;  it  may  however  be  remarked,  that  here  the 
greatest  stupidity  is  the  most  successful. 

bth  May,  1761. 


LETTER  XL 

Reflections  on  Divisibility  in  infinitum,  and  on  Monads. 

IN  speaking  of  the  divisibility  of  body,  we  must 
carefully  distinguish  what  is  in  our  power,  from 
what  is  possible  in  itself.  In  the  first  sense,  it  can- 
not be  denied  that  such  a  division  of  body  as  we  are 
capable  of  must  be  very  limited. 

By  pounding  a  stone  we  can  easily  reduce  it  to 
powder ;  and  if  it  were  possible  to  reckon  all  the 
little  grains  which  form  that  powder,  their  number 
would  undoubtedly  be  so  great,  that  it  would  be 
matter  of  surprise  to  have  divided  the  stone  into  so 
many  parts.  But  these  very  grains  will  be  almost 
indivisible  with  respect  to  us,  as  no  instrument  wo 
could  employ  will  be  able  to  lay  hold  of  them.  But 


AND    ON   MONADS.  43 

it  cannot  with  truth  be  affirmed  that  they  are  indi- 
visible in  themselves.  You  have  only  to  view  them 
with  a  good  microscope,  and  each  will  appear  itself 
a  considerable  stone,  on  which  are  distinguishable  a 
great  many  points  and  inequalities ;  which  demon- 
strates the  possibility  of  a  further  division,  though 
we  are  not  in  a  condition  to  execute  it.  For  wher- 
ever we  can  distinguish  several  points  in  any  object, 
it  must  be  divisible  in  so  many  parts. 

We  speak  not,  therefore,  of  a  division  practicable 
by  our  strength  and  skill,  but  of  that  which  is  pos- 
sible in  itself,  and  which  the  Divine  Omnipotence  is 
able  to  accomplish. 

It  is  in  this  sense,  accordingly,  that  philosophers 
use  the  word  "  divisibility :"  so  that  if  there  were  a 
stone  so  hard  that  no  force  could  break  it,  it  might 
be  without  hesitation  affirmed  that  it  is  as  divisible 
in  its  own  nature  as  the  most  brittle  of  the  same 
magnitude.  And  how  many  bodies  are  there  on 
which  we  cannot  lay  any  hold,  and  of  whose  divisi- 
bility we  can  entertain  not  the  smallest  doubt  ?  No 
one  doubts  that  the  moon  is  a  divisible  body,  though 
he  is  incapable  of  detaching  the  smallest  particle 
from  it :  and  the  simple  reason  for  its  divisibility  is 
its  being  extended. 

Wherever  we  remark  extension,  we  are  under  the 
necessity  of  acknowledging  divisibility,  so  that  di- 
visibility is  an  inseparable  property  of  extension. 
But  experience  likewise  demonstrates  that  the  divi- 
sion of  bodies  extends  very  far.  I  shall  not  insist 
at  great  length  on  the  instance  usually  produced  of 
a  ducat :  the  ai  tisan  can  beat  it  out  into  a  leaf  so 
fine  as  to  cover  a  very  large  surface,  and  the  ducat 
may  be  divided  into  as  many  parts  as  that  surface  is 
capable  of  being  divided.  Our  own  body  furnishes 
an  example  much  more  surprising.  Only  consider 
the  delicate  veins  and  nerves  with  which  it  is  filled, 
and  the  fluids  which  circulate  through  them.  The 
eubtilty  there  discoverable  far  surpasses  imagination. 


44  REFLECTIONS    ON   DIVISIBILITY, 

The  smallest  insects,  such  as  are  scarcely  visible 
lo  the  naked  eye  have  all  their  members,  and  legs 
on  which  they  walk  with  amazing  velocity     Hence 
we  see  that  each  limb  has  its  muscles  composed  of  a 
great  number  of  fibres;  that  they  have  veins  and 
nerves  and  a  fluid  still  much  more  subtile  which 
flows  through  their  whole  extent. 
,       On  viewing  with  a  good  microscope  a  single  drop 
of  water,  it  has  the  appearance  of  a  sea;  we  see 
thousands  of  living  creatures  swimming  in  it,  each 
)f  which  is  necessarily  composed  of  an  infinite  num- 
ber of  muscular  and  nervous  fibres,  whose  marvel- 
lous structure  ought  to  excite  our  admiration  *  And 
though  these  creatures  may  perhaps  be  the  smallest 
which  we  are  capable  of  discovering  by  the  help  of 
ie  microscope  undoubtedly  they  are  not  the  small- 
ist  which  the  Creator  has  produced.     Animalcules 
probably  exist  as  small  relatively  to  them  as  they 
are  relatively  to  us.     And  these  after  all  are  not  yet 
the  smallest,  but  may  be  followed  by  an  infinity  of 
new  classes,  each  of  which  contains  creatures  in- 
™amsparablv  smaller  than  those  of  the  preceding 

We  ought  in  this  to  acknowledge  the  omnipotence 
and  infinite  wisdom  of  the  Creator,  as  in  objects  of 
the  greatest  magnitude.  It  appears  to  me  that  the 
consideration  of  these  minute  species,  each  of  which 
;  followed  by  another  inconceivably  more  minute, 
ought  to  make  the  liveliest  impression  on  our  minds 
and  inspire  us  with  the  most  sublime  ideas  of  the 

found"  ^T  °f  animal8  °f  S,uperior  ma?nitude,  called  medusas,  has  been 
Sd  the  nTm°hUS  "  ?„  dU,C-OlOIlr  the  °Cean  itself'     Captain  Scoresby 
1      e  ollv- 


d  the  nmh  „       ,-  '  esy 

inrh  rnn    '     *£       21      e  ollve-green    8ea  to  be  immense.     A  cubic 
OOOOOOoSnS   VhndC°nSeqUentlyacubic  mile  would  contain  23,888- 
could  >o2  ,  ?  mJ     *ame  CmTnt  naviSator  remarks,  that  if  one  persok 
S«2nT«hnnl^  h        '"  SeVT  dayS'  k  WOUld  have  required  that  80,000 
*n,  J      re  StartKd  at  the  creation  of  the  w°rld  to  have  com- 
epn"meratlon  at  ^  Present  time.-See  Scoresby's  Account  of 

«-  Mt 


AND   ON   MONADS.  45 

works  of  the  Almighty,  whose  power  knows  no 
bounds,  whether  as  to  great  objects  or  small. 

To  imagine,  that  after  having  divided  a  body  into 
a  great  number  of  parts,  we  arrive  at  length  at  par- 
ticles so  small  as  to  defy  all  further  division,  is  there- 
fore the  indication  of  a  very  contracted  mind.  But 
supposing  it  possible  to  descend  to  particles  so  mi- 
nute as  to  be,  in  their  own  nature,  no  longer  divisi- 
ble, as  in  the  case  of  the  supposed  monads  ;  before 
coming  to  this  point,  we  shall  have  a  particle  com- 
posed of  only  two  monads,  and  this  particle  will  be 
of  a  certain  magnitude  or  extension,  otherwise  it 
could  not  have  been  divisible  into  these  two  monads. 
Let  us  further  suppose  that  this  particle,  as  it  has 
some  extension,  may  be  the  thousandth  part  of  an 
inch,  or  still  smaller  if  you  will — for  it  is  of  no  im- 
portance ;  what  I  say  of  the  thousandth  part  of  an 
inch  may  be  said  with  equal  truth  of  every  smaller 
part.  This  thousandth  part  of  an  inch,  then,  is  com- 
posed of  two  monads,  and  consequently  two  monads 
together  would  be  the  thousandth  part  of  an  inch, 
and  two  thousand  times  nothing  a  whole  inch ;  the 
absurdity  strikes  at  first  sight. 

The  partisans  of  the  system  of  monads  accordingly 
shrink  from  the  force  of  this  argument,  and  are  re- 
duced to  a  terrible  nonplus  when  asked  how  many 
monads  are  requisite  to  constitute  an  extension. 
Two,  they  apprehend,  would  appear  insufficient, 
they  therefore  allow  that  more  must  be  necessary. 
But  if  two  monads  cannot  constitute  extension,  as 
each  of  the  two  has  none,  neither  three,  nor  four, 
nor  any  number  whatever  will  produce  it ;  and  this 
Completely  subverts  the  system  of  monads. 

QthMay,  1761. 


46  REPLY    TO   THE    OBJECTIONS    OF 


LETTER  XII. 

Reply  to  the  Objections  of  the  Monadists  to  Divisibility 
in  infinitum. 

THE  partisans  of  monads  are  far  from  submitting 
to  the  arguments  adduced  to  establish  the  divisibility 
of  body  to  infinity.  Without  attacking  them  directly, 
they  allege  that  divisibility  in  infinitum  is  a  chi- 
mera of  geometricians,  and  that  it  is  involved  in  con- 
tradiction. For  if  each  body  is  divisible  to  infinity, 
it  would  contain  an  infinite  number  of  parts,  the 
smallest  bodies  as  well  as  the  greatest ;  the  number 
of  these  particles  to  which  divisibility  in  infinitum 
would  lead,  that  is  to  say,  the  most  minute  of  which 
bodies  are  composed,  will  then  be  as  great  in  the 
smallest  body  as  in  the  largest,  this  number  being 
infinite  in  both;  and  hence  the  partisans  of  monads 
triumph  in  their  reasoning  as  invincible.  For  if  the 
number  of  ultimate  particles  of  which  two  bodies 
are  composed  is  the  same  in  both,  it  must  follow, 
say  they,  that  the  bodies  are  perfectly  equal  to  each 
other. 

Now  this  goes  on  the  supposition  that  the  ulti- 
mate particles  are  all  perfectly  equal  to  each  other ; 
for  if  some  were  greater  than  others,  it  would  not  be 
surprising -that  one  of  the  two  bodies  should  be  much 
greater  than  the  other.  But  it  is  absolutely  neces- 
sary, say  they,  that  the  ultimate  particles  of  all 
bodies  should  be  equal  to  each  other,  as  they  no 
longer  have  any  extension,  and  their  magnitude  abso- 
lutely vanishes,  or  becomes  nothing.  They  even 
form  a  new  objection,  by  alleging  that  all  bodies 
would  be  composed  of  an  infinite  number  of  nothings, 
which  is  a  still  greater  absurdity. 

I  readily  admit  this ;  but  I  remark,  at  the  same 
time,  that  it  ill  becomes  them  to  raise  such  an  ob- 


THE    MONADISTS    TO   DIVISIBILITY.  47 

jection,  seeing  they  maintain  that  all  bodies  are 
composed  of  a  certain  number  of  monads,  though, 
relatively  to  magnitude,  they  are  absolutely  nothings: 
so  that  by  their  own  confession  several  nothings  are 
capable  of  producing  a  body.  They  are  right  in 
saying  their  monads  are  not  nothings,  but  beings 
endowed  with  an  excellent  quality,  on  which  the  na- 
ture of  the  bodies  which  they  compose  is  founded. 
Now,  the  only  question  here  is  respecting  extension ; 
and  as  they  are  under  the  necessity  of  admitting  that 
the  monads  have  none,  several  nothings,  according 
to  them,  would  always  be  something. 

But  I  shall  push  this  argument  against  the  system 
of  monads  no  farther ;  my  object  being  to  make  a 
direct  reply  to  the  objection  founded  on  the  ultimate 
particles  of  bodies,  raised  by  the  monadists  in  sup- 
port of  their  system,  by  which  they  flatter  themselves 
in  the  confidence  of  a  complete  victory  over  the 
partisans  of  divisibility  in  infinitum. 

I  should  be  glad  to  know,  in  the  first  place,  what 
they  mean  by  the  ultimate  particles  of  bodies.  In 
their  system,  according  to  which  every  body  is  com- 
posed of  a  certain  number  of  monads,  I  clearly  com- 
prehend that  the  ultimate  particles  of  a  body  are  the 
monads  themselves  which  constitute  it ;  but  in  the 
system  of  divisibility  in  infinitum,  the  term  ultimate 
particle  is  absolutely  unintelligible. 

They  are  right  in  saying,  that  these  are  the  pai 
tides  at  which  we  arrive  from  the  division  of  bodies, 
after  having  continued  it  to  infinity.  But  this  is 
just  the  same  thing  with  saying,  after  having  finished 
a  division  which  never  comes  to  an  end.  For  divisi- 
bility in  infinitum  means  nothing  else  but  the  pos- 
sibility of  always  carrying  on  the  division,  without 
ever  arriving  at  the  point  where  it  would  be  neces- 
sary to  stop.  He  who  maintains  divisibility  in  in- 
finitum boldly  denies,  therefore,  the  existence  of  the 
ultimate  particles  of  body;  and  it  is  a  manifest  con- 


STRONGEST    SUPPORT 

tradiction  to  suppose  at  once  ultimate  particles  and 
divisibility  in  infinitum. 

I  reply,  then,  to  the  partisans  of  the  system  of 
monads,  that  their  objection  to  the  divisibility  of 
body  to  infinity  would  be  a  very  solid  one,  did  that 
system  admit  of  ultimate  particles;  but  being  ex- 
pressly excluded  from  it,  all  this  reasoning  of  course 
falls  to  the  ground. 

It  is  false,  therefore,  that  in  the  system  of  divisi- 
bility in  infinitum  bodies  are  composed  of  an  infinity 
of  particles.  However  closely  connected  these  two 
propositions  may  appear  to  the  partisans  of  monads, 
they  manifestly  contradict  each  other ;  for  whoever 
maintains  that  body  is  divisible  in  infinitum,  or  with- 
out end,  absolutely  denies  the  existence  of  ultimate 
particles,  and  consequently  has  no  concern  in  the 
question.  The  term  can  only  mean  such  particles  as 
are  no  longer  divisible— an  idea  totally  inconsistent 
with  the  system  of  divisibility  in  infinitum.  This 
formidable  attack,  then,  is  completely  repelled 

LETTER  XIII, 

Principle  of  the  Sufficient  Reason,  the  strongest  Support 
of  the  Monadists. 

You  must  be  perfectly  sensible  that  one  of  the  two 
systems  which  have  undergone  such  ample  discus- 
sion is  necessarily  true,  and  the  other  false,  seeing 
they  are  contradictory. 

It  is  admitted  on  both  sides  that  bodies  are  divisi- 
ble ;  the  only  question  is,  Whether  this  divisibility 
is  limited  ?  or,  Whether  it  may  always  be  carried 
further,  without  the  possibility  of  ever  arriving-  at 
indivisible  particles  1 

The  system  of  monads  is  established  in  the  former 
case,  since  after  having  divided  a  body  into  indivisi- 


OF    THE    MONADISTS.  49 

ble  particles,  these  very  particles  are  monads,  and 
there  would  be  reason  for  saying  that  all  bodies  are 
composed  of  them,  and  each  of  a  certain  determinate 
number.  Whoever  denies  the  system  of  monads 
must  likewise,  then,  deny  that  the  divisibility  of 
bodies  is  limited.  He  is  under  the  necessity  of 
maintaining  that  it  is  always  possible  to  carry  this 
divisibility  further,  without  ever  being  obliged  to 
stop ;  and  this  is  the  case  of  divisibility  in  infinitum, 
on  which  system  we  absolutely  deny  the  existence 
of  ultimate  particles ;  consequently  the  difficulties 
resulting  from  their  infinite  number  fall  to  the  ground 
of  themselves.  In  denying  monads,  it  is  impossible 
to  talk  any  longer  of  ultimate  particles,  and  still  less 
of  the  number  of 'them  which  enters  into  the  com- 
position of  each  body. 

You  must  have  remarked  that  what  t  have  hitherto 
produced  in  support  of  the  system  of  monads  is  des- 
titute of  solidity.  I  now  proceed  to  inform  you,  that 
its  supporters  rest  their  cause  chiefly  on  the  great 
principle  of  the  sufficient  reason,  which  they  know 
how  to  employ  so  dexterously  that  by  means  of  it 
they  are  in  a  condition  to  demonstrate  whatever 
suits  their  purpose,  and  to  demolish  whatever  makes 
against  them.  The  great  discovery  made,  then,  is 
this,  That  nothing  can  be  without  a  sufficient  reason : 
and  to  modern  philosophers  we  stand  indebted  for  it. 

In  order  to  give  you  an  idea  of  this  principle,  you 
have  only  to  consider,  that  in  every  thing  presented 
to  you,  it  may  always  be  asked,  Why  is  it  such? 
And  the  answer  is,  what  they  call  the  sufficient  rea- 
son, supposing  it  really  to  correspond  with  the  ques- 
tion proposed.  Wherever  the  why  can  take  place, 
the  possibility  of  a  satisfactory  answer  is  taken  for 
granted,  which  shall,  of  course,  contain  the  sufficient 
reason  of  the  thing. 

This  is  very  far,  however,  from  being  a  mystery 
of  modern  discovery.  Men  in  every  age  have  asked 
why— an  incontestable  proof  of  their  conviction  that 

VOL.  II.— E 


50  STRONGEST   SUPPORT 

every  thing  must  have  a  satisfying  reason  of  its  ex- 
istence. This  principle,  that  nothing  is  without  a  cause, 
was  very  well  known  to  ancient  philosophers  ;  but 
unhappily  this  cause  is  for  the  most  part  concealed 
from  us.  To  little  purpose  do  we  ask  why ;  no  one 
is  qualified  to  assign  the  reason.  It  is  not  a  matter 
of  doubt  that  every  thing  has  its  cause  ;  but  a  pro- 
gress thus  far  hardly  deserves  the  name ;  and  so  long 
as  it  remains  concealed,  we  have  not  advanced  a 
single  step  in  real  knowledge. 

You  may  perhaps  imagine  that  modern  philoso- 
phers, who  make  such  a  boast  of  the  principle  of  a 
sufficient  reason,  have  actually  discovered  that  of  all 
things,  and  are  in  a  condition  to  answer  every  why 
that  can  be  proposed  to  them ;  which  would  un- 
doubtedly be  the  very  summit  of  human  knowledge  : 
but  in  this  respect  they  are  just  as  ignorant  as  their 
neighbours ;  their  whole  merit  amounts  to  no  more 
than  a  pretension  to  have  demonstrated,  that  wher- 
ever it  is  possible  to  ask  the  question  why,  there 
must  be  a  satisfactory  answer  to  it,  though  concealed 
from  us. 

They  readily  admit  that  the  ancients  had  a  know- 
ledge of  this  principle,  but  a  knowledge  very  ob- 
scure ;  whereas  they  pretend  to  have  placed  it  in  its 
clearest  light,  and  to  have  demonstrated  the  truth  ot 
it  •  and  therefore  it  is  that  they  know  how  to  turn  it 
most  to  their  account,  and  that  this  principle  puts 
them  in  a  condition  to  prove  that  bodies  are  com- 
posed of  monads. 

Bodies,  say  they,  must  have  their  sufficient  reason 
somewhere ;  but  if  they  were  divisible  to  infinity, 
such  reason  could  not  take  place ;  and  hence  they 
conclude,  with  an  air  altogether  philosophical,  that 
as  every  thing  must  have  its  sufficient  reason,  it  ts 
absolutely  necessary  that  all  bodies  should  le  composed 
of  monads— which  was  to  be  demonstrated.  1  his,  1 
must  admit,  is  a  demonstration  not  to  be  resisted. 
It  were  greatly  to  be  wished  that  a  reasoning  so 


OF   THE    MONADISTS.  51 

slight  could  elucidate  to  us  questions  of  this  import- 
ance ;  but  I  frankly  confess  I  comprehend  nothing 
of  the  matter.  They  talk  of  the  sufficient  reason 
of  bodies,  by  which  they  mean  to  reply  to  a  certain 
wherefore,  which  remains  unexplained.  But  it  would 
be  proper,  undoubtedly,  clearly  to  understand  and 
carefully  to  examine  a  question,  before  a  reply  is 
attempted ;  in  the  present  case,  the  answer  is  given 
before  the  question  is  formed. 

Is  it  asked,  Why  do  bodies  exist  ?  It  would  be 
ridiculous,  in  my  opinion,  to  reply,  Because  they  are 
composed  of  monads ;  as  if  they  contained  the  cause 
of  that  existence.  Monads  have  not  created  bodies ; 
and  when  I  ask,  Why  such  a  being  exists  T:  I  see  no 
other  reason  that  can  be  given  but  this,  Because  the 
Creator  has  given  it  existence  ;  and  as  to  the  man- 
ner in  which  creation  is  performed,  philosophers,  I 
think,  would  do  well  honestly  to  acknowledge  their 
ignorance. 

But  they  maintain,  that  God  could  not  have  pro- 
duced bodies  without  having  created  monads,  which 
were  necessary  to  form  the  composition  of  them. 
This  manifestly  supposes  that  bodies  are  composed 
of  monads,  the  point  which  they  meant  to  prove  by 
this  reasoning.  And  you  are  abundantly  sensible, 
that  it  is  not  fair  reasoning  to  take  for  granted  the 
truth  of  a  proposition  which  you  are  bound  to  prove 
by  reasoning.  It  is  a  sophism  known  in  logic  by 
the  name  of  a  petitio  principii,  or  begging  the  quea 
tion. 

Wth  May,  1761, 


52  ANOTHER  ARGUMENT 


LETTER  XIV. 

Another  Argument  of  the  Monadists,  derived  from  the 
Principle  of  the  Sufficient  Reason.  Absurdities  re- 
sulting from  it. 

THE  partisans  of  monads  likewise  derive  their 
grand  argument  from  the  principle  of  the  sufficient 
reason,  by  alleging  that  they  could  not  even  com- 
prehend the  possibility  of  bodies,  if  they  were  divisi- 
ble to  infinity,  as  there  would  be  nothing  in  them 
capable  of  checking  imagination ;  they  must  have 
ultimate  particles  or  elements,  the  composition  of 
which  must  serve  to  explain  the  composition  of 
bodies. 

But  do  they  pretend  to  understand  the  possibility 
of  all  the  things  which  exist  ?  This  would  savour 
too  much  of  pride  ;  nothing  is  more  common  among 
philosophers  than  this  kind  of  reasoning — I  cannot 
comprehend  the  possibility  of  this,  unless  it  is  such 
as  I  imagine  it  to  be :  therefore  it  necessarily  must 
be  such. 

You  clearly  comprehend  the  frivolousness  of  such 
reasoning ;  and  that  in  order  to  arrive  at  truth,  re- 
search much  more  profound  must  be  employed.  Ig- 
norance can  never  become  an  argument  to  conduct 
us  to  the  knowledge  of  truth,  and  the  one  in  question 
is  evidently  founded  on  ignorance  of  the  different 
manners  which  may  render  the  thing  possible. 

But  on  the  supposition  that  nothing  exists  but  that 
whose  possibility  they  are  able  to  comprehend,  is  it 
possible  for  them  to  explain  how  bodies  would  be 
composed  of  monads !  Monads,  having  no  exten- 
sion, must  be  considered  as  points  in  geometry,  or 
as  we  represent  to  ourselves  spirits  and  souls.  Now 
it  is  well  known  that  many  geometrical  points,  let 
the  number  be  supposed  ever  so  great,  never  can 


OF    THE    MONADISTS.  53 

produce  a  line,  and  consequently  still  less  a  surface, 
or  a  body.  If  a  thousand  points  were  sufficient  to 
constitute  the  thousandth  part  of  an  inch,  each  of 
these  must  necessarily  have  an  extension,  which 
taken  a  thousand  times  would  become  equal  to  the 
thousandth  part  of  an  inch.  Finally,  it  is  an  incon- 
testable truth,  that  take  any  number  of  points  you 
will,  they  can  never  produce  extension.  I  speak  here 
of  points  such  as  we  conceive  in  geometry,  without 
any  length,  breadth,  or  thickness,  and  which  in  that 
respect  are  absolutely  nothing. 

Our  philosophers  accordingly  admit  that  no  ex- 
tension can  be  produced  by  geometrical  points,  and 
they  solemnly  protest  that  their  monads  ought  not 
to  be  confounded  with  these  points.  They  have  no 
more  extension  than  points,  say  they ;  but  they  are 
invested  with  admirable  qualities,  such  as  represent- 
ing to  them  the  whole  universe  by  ideas,  though  ex- 
tremely obscure ;  and  these  qualities  render  them 
proper  to  produce  the  phenomenon  of  extension,  or 
rather  that  apparent  extension  which  I  formerly 
mentioned.  The  same  idea,  then,  ought  to  be 
formed  of  monads  as  of  spirits  and  souls,  with  this 
difference,  that  the  faculties  of  monads  are  much 
more  imperfect. 

The  difficulty  appears  to  me  by  this  greatly  in- 
creased ;  and  I  flatter  myself  you  will  be  of  my 
opinion  that  two  or  more  spirits  cannot  possibly  be 
joined  so  as  to  form  extension.  Several  spirits  may 
very  well  form  an  assembly  or  a  council,  but  never 
an  extension ;  abstraction  made  of  the  body  of  each 
counsellor,  which  contributes  nothing  to  the  delibe- 
ration going  forward,  for  this  is  the  production  of 
spirits  only ;  a  council  is  nothing  else  but  an  assem- 
bly of  spirits  or  souls :  but  could  such  an  assembly 
represent  an  extension]  Hence  it  follows  that 
monads  are  still  less  proper  to  produce  extension 
than  geometrical  points  are. 

The  partisans  of  the  system,  accordingly,  are  not 
E2 


54  ARGUMENT    OF    THE    MONADISTS. 

agreed  as  to  this  point.  Some  allege,  that  monads 
are  actual  parts  of  bodies ;  and  that  after  having 
divided  a  body  as  far  as  possible,  you  then  arrive  at 
the  monads  which  constitute  it. 

Others  absolutely  deny  that  monads  can  be  con- 
sidered as  constituent  parts  of  bodies ;  according  to 
them,  they  contain  only  the  sufficient  reason :  while 
the  body  is  in  motion,  the  monads  do  not  stir,  but 
they  contain  the  sufficient  reason  of  motion.  Finally, 
they  cannot  touch  each  other ;  thus,  when  my  hand 
touches  a  body,  no  one  monad  of  my  hand  touches 
a  monad  of  the  body. 

What  is  it  then,  you  will  ask,  that  touches  in  this 
case,  if  it  is  not  the  monads  which  compose  the  hand 
and  the  body  T  The  answer  must  be,  that  two  no- 
things touch  each  other,  or  rather  it  must  be  denied 
that  there  is  a  real  contact.  It  is  a  mere  illusion, 
destitute  of  all  foundation.  They  are  under  the  ne- 
cessity of  affirming  the  same  thing  of  all  bodies, 
which,  according  to  these  philosophers,  are  only 
phantoms  formed  by  the  imagination,  representing 
to  itself  very  confusedly  the  monads  which  contain 
the  sufficient  reason  of  all  that  we  denominate  body. 

In  this  philosophy  every  thing  is  spirit,  phantom, 
and  illusion ;  and  when  we  cannot  comprehend  these 
mysteries,  it  is  our  stupidity  that  keeps  up  an  attach- 
ment to  the  gross  notions  of  the  vulgar. 

The  greatest  singularity  in  the  case  is,  that  these 
philosophers,  with  a  design  to  investigate  and  explain 
the  nature  of  bodies  and  of  extension,  are  at  last  re- 
duced to  deny  their  existence.  This  is  undoubtedly 
the  surest  way  to  succeed  in  explaining  the  phe- 
nomena of  nature  ;  you  have  only  to  deny  them,  and 
to  allege  in  proof  the  principle  of  the  sufficient  rea- 
son. Into  such  extravagances  will  philosophers  run 
rather  than  acknowledge  their  ignorance. 
19th  May,  1761.- 


SYSTEM    OF   MONADS.  55 

LETTER  XV. 

Reflections  on  the  System  of  Monads. 

IT  would  be  a  great  pity,  however,  that  this  inge- 
nious system  of  monads  should  crumble  into  ruins. 
It  has  made  too  much  noise,  it  has  cost  its  partisans 
too  many  sublime  and  profound  speculations,  to  be 
permitted  to  sink  into  total  oblivion.  It  will  evei 
remain  a  striking  monument  of  the  extijavagance 
into  which  the  spirit  of  philosophizing  may  run.  It 
is  well  worth  while,  then,  to  present  you  with  a  more 
particular  account  of  it. 

It  is  necessary,  first  of  all,  to  banish  from  the  mind 
every  thing  corporeal — all  extension,  all  motion,  all 
time  and  space—for  all  these  are  mere  illusion. 
Nothing  exists  in  the  world  but  monads,  the  number 
of  which  undoubtedly  is  prodigious.  No  one  monad 
is  to  be  found  in  connexion  with  others ;  and  it  is 
demonstrated  by  the  principle  of  the  sufficient  rea- 
son that  monads  can  in  no  manner  whatever  act 
upon  each  other.  They  are  indeed  invested  with 
powers,  but  these  are  exerted  only  within  themselves, 
without  having  the  least  influence  externally. 

These  powers,  with  which  each  monad  is  endowed, 
have  a  tendency  only  to  be  continually  changing 
their  own  state,  and  consist  in  the  representation  of 
all  other  monads.  My  soul,  for  example,  is  a  mo- 
nad, and  contains  in  itself  ideas  of  the  state  of  all 
other  monads.  These  ideas  are  for  the  most  part 
very  obscure ;  but  the  powers  of  my  soul  are  con- 
tinually employed  in  their  further  elucidation,  and 
in  carrying  them  to  a  higher  degree  of  clearness. 
Other  monads  have,  in  this  respect,  a  sufficient  re- 
semblance to  my  soul;  each  is  replete  with  a  pro- 
digious quantity  of  obscure  ideas  of  all  other  monads, 
and  of  their  state ;  and  they  are  continually  exerting 


REFLECTIONS    ON    THE 

themselves  with  more  or  less  success  in  unfolding- 
ofcle        * '  and  ln  carrying  them  to  a  hi£her  degree 
Such  monads  as  have  succeeded  better  than  I  have 
one  are  spirits  more  perfect;  but  the  greater  part 
11  remain  in  a  state  of  stagnation,  in  the  greatest 
obscurity  of  their  ideas ;  and  when  they  are  the  ob- 
ject of  the  ideas  of  my  soul,  they  produce  in  it  the 
illusory  and  chimerical  idea  of  extension  and  of 
body.     As  often  as  my  soul  thinks  of  bodies  and  of 
ration,  this  proves  that  a  great  quantity  of  other 
monads  are  still  buried  in  their  obscurity;  it  is  like- 
wise when  I  think  of  them  that  my  soul  forms  within 
the  idea  of  some  extension,  which  is  conse- 
quently nothing  but  mere  illusion. 

The  more  monads  there  are  plunged  in  the  abyss 
of  the  obscurity  of  their  ideas,  the  more  is  my  soul 
dazzled  with  the  idea  of  extension  ;  but  when  they 
come  to  clear  up  their  obscure  ideas,  extension  seems 
;o  me  to  dimmish,  and  this  produces  in  my  soul  the 
illusory  idea  of  motion. 

n,TOUuWi11  ask'  no  doubt'  how  mY  soul  perceives 
that  other  monads  succeed  in  developing  their  obscure 
ideas,  seeing  there  is  no  connexion  between  them 
and  me  The  partisans  of  the  system  of  monads 
are  ready  with  this  reply,  that  it  takes  place  conform- 
ably to  the  perfect  harmony  which  the  Creator  (who 
s  himself  only  a  monad)  has  established  between 
monads,  by  which  each  perceives  in  itself,  as  in  a 
mirror,  every  development  produced  in  others,  with- 
out any  manner  of  connexion  between  them. 

t  is  to  be  hoped,  then,  that  all  monads  may  at 
length  become  so  happy  as  to  clear  up  their  obscure 
ideas,  and  then  we  should  lose  all  ideas  of  body  and 
of  motion ;  and  the  illusion,  arising  merely  from  the 
obscurity  of  ideas,  would  entirely  cease.  * 

But  there  is  little  appearance  of  the  arrival  of  this 
blessed  state ;  most  monads,  after  having  acquired 
the  capacity  of  clearing  up  their  obscure  ideas,  sud- 


SYSTEM    OF    MONADS.  57 

denly  relapse.  When  shut  up  in  my  chamber,  I 
perceive  myself  but  of  small  extension,  because 
several  monads  have  then  unfolded  their  ideas ;  but  as 
soon  as  I  walk  abroad,  and  contemplate  the  vast  ex- 
panse of  heaven,  they  must  all  have  relapsed  into 
their  state  of  dulness. 

There  is  no  change  of  place  or  of  motion;  all 
that  is  illusion  merely:  my  soul  remains  almost 
always  in  the  same  place,  just  as  all  other  monads. 
But  when  it  begins  to  unfold  some  ideas  which 
before  were  but  very  obscure,  it  appears  to  me  then 
that  I  am  approaching  the  object  which  they  repre- 
sent to  me,  or  rather  that  which  the  monads  of  such 
idea  excite  in  me ;  and  this  is  the  real  explanation 
of  the  phenomenon,  when  it  appears  to  us  that  we 
are  approaching  to  certain  objects. 

It  happens  but  too  frequently  that  the  elucida- 
tions we  had  acquired  are  again  lost ;  then  it  appears 
to  us  that  we  are  removing  from  the  same  object. 
And  here  we  must  look  for  the  true  solution  of  our 
journeyings.  My  idea,  for  example,  of  the  city  of 
Magdeburg  is  produced  by  certain  monads,  of  which 
at  present  I  have  but  very  obscure  ideas  ;  and  this 
is  the  reason  why  I  consider  myself  as  at  a  distance 
from  Magdeburg.  Last  year  these  same  ideas  sud- 
denly became  clear,  and  then  I  imagined  I  was 
travelling  to  Magdeburg,  and  that  I  remained  there 
several  days.  This  journey,  however,  was  an  illu- 
sion merely,  for  my  soul  never  stirs  from  its  place. 
It  is  likewise  an  illusion  when  you  imagine  yourself 
absent  from  Berlin,  because  the  confused  repre- 
sentation of  certain  monads  excites  an  obscure  idea 
of  Berlin,  which  you  have  only  to  clear  up,  and  that 
instant  you  are  at  Berlin.  Nothing  more  is  neces- 
sary. What  we  call  journeys,  and  on.  which  we 
expend  so  much  money,  is  mere  illusion.  Such  is 
the  real  plan  of  the  system  of  monads. 

You  will  ask,  Is  it  possible  there  ever  should  have 
been  persons  of  good  sense  who  seriously  maintained 


58  REFLECTIONS    ON    THE 

these  extravagances  1    I  reply,  there  have  been  but 
too  many,  that  I  know  several  of  them,  that  there 
are  some  at  Berlin,  nay,  perhaps  at  Magdeburg. 
23d  May,  1761. 

LETTER  XVI. 

Continuation. 

THE  system  of  monads,  such  as  I  have  been  de- 
scribing it,  is  a  necessary  consequence  from  the 
principle  that  bodies  are  compounded  of  simple 
beings.  The  moment  this  principle  is  admitted, 
you  are  obliged  to  acknowledge  the  justness  of  all 
the  other  consequences,  which  result  from  it  so 
naturally  that  it  is  impossible  to  reject  any  one, 
however  absurd  and  contradictory. 

First,  these  simple  beings,  which  must  enter  into 
the  composition  of  bodies,  being  monads  which  have 
no  extension,  neither  can  their  compounds,  that  is 
bodies,  have  any;  and  all  these  extensions  become 
illusion  and  chimera,  it  being  certain  that  parts  des- 
titute of  extension  are  incapable  of  producing  a  real 
extension ;  it  can  be  at  most  an  appearance  c 
phantom,  which  dazzles  by  a  fallacious  idea  of  exten- 
sion. In  a  word,  every  thing  becomes  illusion ;  and 
upon  this  is  founded  the  system  of  pre-established 
harmony,  the  difficulties  of  which  I  have  already 

P°lfis  $ecessary  then  to  take  care  that  we  be  not 
entangled  in  this  labyrinth  of  absurdities  If  you 
makel  single  false  step  over  the  threshold,  you  are 
involved  beyond  the  power  of  escaping.  Iwery 
thing  depends  on  the  first  ideas  formed  of  extension : 
and  the  manner  in  which  the  partisans  of  the  system 
of  monads  endeavour  to  establish  it  is  extremely 


-i  nese  pnuusupu™  do  not  like  to  speak  of  the  ex- 
tension of  bodies,  because  they  clearly  foresee  that 


SYSTEM    OF    MONADS.  59 

it  must  become  fatal  to  them  in  the  sequel;  but 
instead  of  saying  that  bodies  are  extended,  they 
denominate  them  compound  beings,  which  no  one 
can  deny,  as  extension  necessarily  supposes  divisi- 
bility, and  consequently  a  combination  of  parts  which 
constitute  bodies.  But  they  presently  make  a  wrong 
use  of  this  notion  of  a  compound  being.  For,  say 
they,  a  being  can  be  compounded  only  so  far  as  it  is 
made  up  of  simple  beings ;  and  hence  they  conclude 
that  every  body  is  compounded  of  simple  beings. 
As  soon  as  you  grant  them  this  conclusion,  you  are 
caught  beyond  the  power  of  retreating ;  for  you  are 
under  the  necessity  of  admitting  that  these  simple 
beings,  not  being  compounded,  are  not  extended. 

This  captious  argument  is  exceedingly  seductive. 
If  you  permit  yourself  to  be  dazzled  with  it,  they 
have  gained  their  point.  Only  admit  this  proposi- 
tion, bodies  are  compounded  of  simple  beings,  that 
is,  of  parts  which  have  no  extension,  and  you  are 
entangled.  With  all  your  might,  then,  resist  this 
assertion — every  compound  being  is  made  up  of  simple 
beings ;  and  though  you  may  not  be  able  directly  to 
prove  the  fallacy,  the  absurd  consequences  which 
immediately  result  would  be  sufficient  to  over- 
throw it. 

In  effect,  they  admit  that  bodies  are  extended; 
from  this  point  the  partisans  of  the  system  of  mo- 
nads set  out  to  establish  the  proposition  that  they 
are  compound  beings ;  and  having  hence  deduced 
that  bodies  are  compounded  of  simple  beings,  they 
are  obliged  to  allow  that  simple  beings  are  incapable 
of  producing  real  extension,  and  consequently  that 
the  extension  of  bodies  is  mere  illusion. 

Ah  argument  whose  conclusion  is  a  direct  con- 
tradiction of  the  premises  is  singularly  strange: 
this  reasoning  sets  out  with  advancing  that  bodies 
are  extended ;  for  if  they  were  not,  how  could  it  be 
known  that  they  are  compound  beings — and  then 
conies  the  conclusion  that  they  are  not  so.  Never 


QO  REFLECTIONS    ON    THE 

was  a  fallacious  argument,  in  my  opinion,  more  com- 
pletely refuted  than  this  has  been  The' question 
was,  Why  are  bodies  extended?  And,  after  a  little 
turning  and  winding,  it  is  answered,  Because  they 
a™™o?so.  Were  I  to  be  asked,  Why  has  a  triangle 
three  sides !  and  I  should  reply  that  it  is  a  mere  illu- 
sion—would such  a  reply  be  deemed  satisfactory  5 

It    is    therefore    certain    that    this   proposition, 
"Every  compound  being- is  necessarily  made  up  ol 
simple  beings,"  leads  to  a  false  conclusion  however 
well  founded  it  may  appear  to  the  partisans  of 
monads,  who  even  pretend  to  rank  it  among  tn< 
axioms  or  first  principles  of   human   knowledge 
The  absurdity  in  which  it  immediately  issues  is  sut- 
ficient  to  overturn  it,  were  there  no  other  reasc 
for  calling  it  in  question. 

But  as  a  compound  being  here  means  the  same 
thing  as  an  extended  being,  it  is  just  as  it  it  were 
affirmed,  "  Every  extended  being  is  compounded  of 
beings  which  are  not  so."  And  this  is  precisely  the 
question.  It  is  asked,  Whether  on  dividing  a  body 
you  arrive  at  length  at  parts  unsusceptible  oi  any 
further  division,  for  want  of  extension ;  or,  Whether 
you  never  arrive  at  particles  such  as  that  the  divis] 
bility  should  be  unbounded  ' 

In  order  to  determine  this  important  question,  lo 
the  sake  of  argument  let  it  be  supposed  that  every 
body  is  compounded  of  parts  without  extension. 
Certain  specious  reasonings  may  easily  be  employed, 
drawn  from  the  noted  principle  of  the  sufficient  rea- 
son ;  and  it  will  be  said  that  a  compound  being  can 
have  its  sufficient  reason  only  in  the  simple  beings 
which  compose  it;  which  might  be  true  if  the  com- 
pound being  were  in  fact  made  up  of  simple  beings, 
the  very  point  in  question;  and  whenever  this  com- 
position is  denied,  the  sufficient  reason  becomes 
totally  inapplicable. 

But  it  is  dangerous  to  enter  the  lists  with  persons 
who  believe  in  monads ;  for,  besides  that  there 


SYSTEM    OF   MONADS.  61 

nothing  to  be  gained,  they  loudly  exclaim  that  you 
are  attacking  the  principle  of  the  sufficient  reason, 
which  is  the  basis  of  all  certainty,  even  of  the  ex- 
istence of  God.  According  to  them,  whoever  refuses 
to  admit  monads,  and  rejects  the  magnificent  fabric, 
in  which  every  thing  is  illusion,  is  an  infidel  and  an 
atheist.  Sure  I  am  that  such  a  frivolous  imputation 
will  not  make  the  slightest  impression  on  your  mind, 
but  that  you  will  perceive  the  wild  extravagances 
into  which  men  are  driven  when  they  embrace  the 
system  of  monads — a  system  too  absurd  to  need  a 
refutation  in  detail ;  their  foundation  being  absolutely 
reduced  to  a  wretched  abuse  of  the  principle  of  the 
sufficient  reason. 
2Gth  May,  1761. 


LETTER  XVII. 

Conclusion  of  Reflections  on  this  System. 

WE  are  under  the  necessity  of  acknowledging  the 
divisibility  of  bodies  in  infinitum,  or  of  admitting  the 
system  of  monads,  with  all  the  extravagances  result- 
ing from  it ;  there  is  no  other  choice — an  alternative 
which  supplies  the  partisans  of  that  system  with 
another  formidable  argument  in  support  of  it. 

They  pretend,  that  by  divisibility  in  infinitum  we 
are  obliged  to  ascribe  to  bodies  an  infinite  quality, 
whereas  it  is  certain  that  God  alone  is  infinite. 

The  partisans  of  the  system  of  monads  are  very 
dangerous  persons ;  they  accused  us  of  atheism,  and 
now  they  charge  us  with  polytheism,  alleging  that 
we  ascribe  to  all  bodies  infinite  perfections.  Thus 
we  should  be  much  worse  than  pagans,  who  only 
worship  certain  idols,  whereas  we  are  accused  of 
paying  homage  to  all  bodies,  as  so  many  divinities. 
A  dreadful  imputation,  no  doubt,  were  it  well 
founded;  and  I  should  certainly  prefer  embracing 

VOL.  II.— F 


62  REFLECTIONS    ON   THE 

the  system  of  monads,  with  all  the  chimeras  and 
illusions  which  flow  from  it,  to  a  declaration  in  favour 
of  divisibility  in  infinitum,  if  it  involved  a  conclusion 
so  impious. 

You  will  allow,  that  to  reproach  one's  adversaries 
with  atheism  or  idolatry  is  a  very  strange  mode  of 
arguing;  but  where  do  they  find  us  ascribing  to 
bodies  this  divine  infinity'?  Are  they  infinitely 
powerful,  wise,  good,  or  happy1?  By  no  means: 
we  only  affirm,  that  on  dividing  bodies,  though  the 
division  be  carried  on  ever  so  far,  it  will  always  be 
possible  to  continue  it  further,  and  that  you  never 
can  arrive  at  indivisible  particles.  It  may  accord- 
ingly be  affirmed,  that  the  divisibility  of  bodies  is 
without  limits ;  and  it  is  improper  to  use  the  term 
infinity,  which  is  applicable  to  God  alone. 

I  must  remark  at  the  same  time,  that  the  word 
"  infinity"  is  not  so  dangerous  as  these  philosophers 
insinuate.  In  saying,  for  example,  infinitely  wicked, 
nothing  is  more  remote  from  the  perfections  of 
God. 

They  admit  that  our  souls  will  never  have  an  end, 
and  thus  Acknowledge  an  infinity  in  the  duration  of 
the  soul,  without  marking  the  least  disrespect  to 
the  infinite  perfections  of  God.  Again,  when  you 
ask  them  if  the  extent  of  the  universe  is  bounded, 
are  they  very  indecisive  in  their  answer  1  Some  of 
them  very  frankly  allow  that  the  extent  of  the  uni- 
verse may  very  probably  be  infinite  without  our 
being  able,  however  far  our  ideas  are  carried,  to 
determine  its  limits.  Here  then  is  one  infinity 
more  which  they  do  not  deem  heretical. 

For  a  still  stronger  reason,  divisibility  in  infinitum 
ought  not  to  give  them  the  least  offence.  To  be 
divisible  to  infinity  is  not  surely  an  attribute  which 
any  one  could  ever  think  of  ascribing  to  the  Supreme 
Being,  and  does  not  confer  on  bodies  a  degree  of 
perfection  which  would  not  be  far  from  that  which 
these  philosophers  allow  them  in  compounding 


SYSTEM   OF    MONADS.  63 

them  of  monads,  which  on  their  system  are  being? 
endowed  with  qualities  so  eminent  that  they  do  not 
hesitate  to  give  to  God  himself  the  denomination  of 
monad. 

In  truth,  the  idea  of  a  division  which  may  be  con 
tinued  without  any  bounds  contains  so  little  of  the 
character  of  the  Deity  that  it  rather  places  bodies 
in  a  rank  far  inferior  to  that  which  spirits  and  our 
souls  occupy ;  for  it  may  well  be  affirmed  that  a 
soul  in  its  essence  is  infinitely  more  valuable  than 
all  the  bodies  in  the  world.  But  on  the  system  of 
monads,  every  body,  even  the  vilest,  is  compounded 
of  a  vast  number  of  monads,  whose  nature  has  a 
great  resemblance  to  that  of  our  souls.  Each  monad 
represents  to  itself  the  whole  world  as  easily  as  our 
souls ;  but,  say  they,  their  ideas  of  it  are  very  ob- 
scure, though  we  have  already  clear,  and  sometimes 
also  distinct  ideas  of  it. 

But  what  assurance  have  they  of  this  difference "? 
Is  it  not  to  be  apprehended  that  the  monads  which 
compose  the  pen  wherewith  I  am  writing  may  have 
ideas  of  the  universe  much  clearer  than  those  of 
my  soul  ?  How  can  I  be  assured  of  the  contrary  1 
I  ought  to  be  ashamed  to  employ  a  pen  in  conveying 
my  feeble  conceptions,  while  the  monads  of  which 
it  consists  possibly  conceive  much  more  sublimely ; 
and  you  might  have  greater  reason  to  be  satisfied, 
should  the  pen  commit  its  own  thoughts  to  paper  in- 
stead of  mine. 

In  the  system  of  monads  that  is  not  necessary ; 
the  soul  represents  to  itself  beforehand,  by  its  in- 
herent powers,  all  the  ideas  of  my  pen,  but  in  a  very 
obscure  manner.  What  I  am  now  taking  the  liberty 
to  suggest  contributes  absolutely  nothing  to  your 
information.  The  partisans  of  this  system  have  de- 
monstrated that  simple  beings  cannot  exercise  the 
slightest  influence  on  each  other ;  and  your  own  soul 
derives  from  itself  what  I  have  been  endeavouring 


64  SYSTEM   OF   MONADS. 

to  convey,  without  my  having  any  concern  in  the 
matter. 

Conversation,  reading,  and  writing,  therefore,  are 
merely  chimerical  and  deceptive  formalities,  which 
illusion  would  impose  upon  us  as  the  means  of  ac- 
quiring and  extending  knowledge.  But  I  have  already 
had  the  honour  of  pointing  out  to  you  the  wonderful 
consequences  resulting  from  the  system  of  the  pre- 
established  harmony ;  and  I  am  apprehensive  that 
these  reveries  may  have  become  too  severe  a  trial 
of  your  patience,  though  many  persons  of  superior 
illumination  consider  this  system  as  the  most  sub- 
lime production  of  human  understanding,  and  are 
incapable  of  mentioning  it  but  with  the  most  pro- 
found respect.* 

30tk  May,  1761. 

*  It  is  a  consolation  to  reflect,  that  philosophy  has  in  modern  times 
divested  itself  of  the  lumber  of  such  idle  disputations  as  those  of  which 
our  author  has  in  the  preceding  Letters  of  this,  and  in  several  of  the 
former,  volume  given  us  so  full  an  account.  The  disputes  about  pre- 
established  harmonies,  and  the  nature  and  existence  of  monads,  and  of 
the  essences  of  things  appear  10  have  been  owing  to  the  want  of  a  just 
conception  of  the  limitation  which  Divine  Providence  has  assigned  to 
the  powers  and  faculties  of  the  human  mind.  Infinity,  whether  in  the 
great  or  in  the  small,  is  absolutely  beyond  our  reach.  That  nature  car- 
ries the  division  of  matter  both  in  the  organic  and  inorganic  world  (as 
the  microscope  reveals  to  us  in  the  astonishing  minuteness  of  animalculae, 
and  as  the  sense  of  smelling  determines  in  the  diffusion  of  odours)  to  an 
extent  beyond  our  comprehension  as  to  the  means  employed,  no  one  can 
doubt;  but  with  respect  to  the  question  of  infinite  divisibility,  about 
which  so  mucli  has  been  said,  although  in  the  abstract  it  may  seem  to  be 
established  in  the  affirmative  by  geometrical  reasoning,  yet  it  is  the  pre- 
vailing opinion  of  the  present  day  that  there  is  a  limitation  in  nature  of 
actual  divisibility.  The  atoms  or  elementary  particles  of  the  chymist 
appear  to  furnish  the  ultimatum  of  the  process  of  nature  in  the  divisibility 
of  matter.  That  different  kinds  of  matter  are  constituted  of  different 
sorts  of  simple  or  elementary  atoms,  having  different  qualities  or  affinities, 
and  that  these  atoms  possess  infinite  hardness,  and  cannot  therefore  be 
further  divided,  are  propositions  which  enable  us  to  account  more  satis- 
factorily for  the  chymical  changes  which  are  constantly  taking  place 
throughout  the  whole  domain  of  nature,  and  for  the  stability  of  the  laws 
to  which  those  changes  are  subservient.  We  know,  indeed,  little  or 
nothing  of  the  real  nature  of  corpuscular  action,  but  the  theory  of  atomic 
combinations  in  stable  and  definite  proportions  has  diffused  a  most  salu- 
tary light  over  the  whole  surface  of  chymical  science.  It  will  be  a  grati- 
fication to  every  Christian  reader  to  observe  the  ability  with  which  Euler 
combats  the  skeptical  philosophy  which  resulted  from  the  visionary  theo- 
ries which  he  has  so  ably  confuted. — Am.  Ed. 


NATURE    OF    COLOURS.  65 

LETTER  XVIII. 

Elucidation  respecting  the  Nature  of  Colours. 

I  AM  under  the  necessity  of  acknowledging,  that 
the  ideas  respecting  colour  which  I  have  already 
taken  the  liberty  to  suggest*  come  far  short  of  that 
degree  of  evidence  to  which  I  could  have  wished  to 
carry  them.  This  subject  has  hitherto  proved  a 
stumbling-block  to  philosophers,  and  I  must  not  flatter 
myself  with  the  belief  that  I  am  able  to  clear  it  of 
every  difficulty.  I  hope,  at  the  same  time,  that  the 
elucidations  which  I  am  going  to  submit  to  your 
examination  may  go  far  towards  removing  a  con- 
siderable part  of  them. 

The  ancient  philosophers  ranked  colours  among 
the  bodies  of  which  we  know  only  the  names.  When 
they  were  asked,  for  example,  why  such  a  body  was 
red,  they  answered,  it  was  in  virtue  of  a  quality  which 
made  it  appear  red.  You  must  be  sensible  that  such 
an  answer  conveys  no  information,  and  that  it  would 
have  been  quite  as  much  to  the  purpose  to  confess 
ignorance. 

Descartes,  who  first  had  the  courage  to  plunge  into 
the  mysteries  of  nature,  ascribes  colours  to  a  certain 
mixture  of  light  and  shade,  which  last,  being  nothing 
else  but  a  want  of  light,  as  it  is  always  found  where 
the  light  does  not  penetrate,  must  be  incapable  of 
producing  the  different  colours  we*  observe. 

Having  remarked  that  the  sensations  of  the  organ 
of  sight  are  produced  by  the  rays  which  strike  that 
organ,  it  necessarily  follows  that  those  which  excite 
in  it  the  sensation  of  red  must  be  of  quite  a  different 
nature  from  those  which  produce  the  sensation  of 
the  other  colours ;  hence  it  is  easily  comprehended 

*  See  Letters  XXVII.,  XXVIII.,  and  XXXI.,  in  vol.  i. 
F3 


66  ELUCIDATION    RESPECTING 

that  each  colour  is  attached  to  a  certain  quality  of 
the  rays  which  strike  the  organ  of  vision.  A  body 
appears  to  us  red  when  the  rays  which  it  emits  are 
of  a  nature  to  excite  in  our  eyes  the  sensation  of 
that  colour. 

The  whole,  then,  results  in  an  inquiry  into  the 
difference  of  the  rays  which  variety  of  colours  pro- 
duces. This  difference  must  be  great  to  produce  so 
many  particular  sensations  in  our  eyes.  But  wherein 
can  it  consist  ]  This  is  the  great  question,  towards 
the  solution  of  which  our  present  research  is  directed. 

The  first  difference  between  rays  which  presents 
itself  is  that  some  are  stronger  than  others.  It  can- 
not be  doubted  that  those  of  the  sun,  or  of  any  other 
body  very  brilliant,  or  very  powerfully  illuminated, 
must  be  much  stronger  than  those  of  a  body  feebly 
illuminated,  or  endowed  with  a  slender  degree  of 
light ;  our  eyes  are  assuredly  struck  in  a  very  differ- 
ent manner  by  the  one  and  by  the  other. 

Hence  it  might  be  inferred,  that  different  colours 
result  from  the  force  of  the  rays  of  light ;  so  that  the 
most  powerful  rays  should  produce,  for  example, 
red ;  those  which  are  less  so,  yellow ;  and  in  pro- 
gression, green,  and  blue. 

But  there  is  nothing  more  easy  than  to  overturn 
this  system,  as  we  know  from  experience  that  the 
same  body  always  appears  to  be  of  the  same  colour, 
be  it  less  or  more  illuminated,  or  whether  its  rays 
be  strong  or  feeble.  A  red  body,  for  example,  ap- 
pears equally  red,  exposed  to  the  brightest  lustre  of 
the  sun,  and  in  the  shade,  where  the  rays  are  ex- 
tremely faint.  We  must  not,  then,  look  for  the 
cause  of  the  difference  of  colour  in  the  different  de- 
grees of  the  force  of  rays  of  light,  it  being  possible 
to  represent  the  same  colour  as  well  by  very  forcible 
as  by  very  faint  rays.  The  feeblest  glimmering 
serves  equally  well  to  discover  to  us  difference  of 
colours,  as  the  brightest  effulgence. 

It  is  absolutely  necessary,  therefore,  that  there 


THE    NATURE    OF   COLOURS.  67 

should  be  another  difference  of  rays  discovered, 
which  may  characterize  their  nature  relatively  to 
the  different  colours.  You  will  undoubtedly  con- 
clude, that  in  order  to  discover  this  difference  we 
must  be  better  acquainted  with  the  nature  of  lumi- 
nous rays ;  in  other  words,  we  must  know  what  it  is 
that,  reaching  our  eyes,  renders  bodies  visible  ;  this 
definition  of  a  ray  must  be  the  justest,  as  in  effect  it 
is  nothing  else  but  that  which  enters  into  the  eye  by 
the  pupil,  and  excites  the  sensation  in  it. 

I  have  already  informed  you  that  there  are  only 
two  systems  or  theories  which  pretend  to  explain 
the  origin  and  nature  of  rays  of  light.  The  one  is 
that  of  Newton,  who  considers  them  as  emanations 
proceeding  from  the  sun  and  other  luminous  bodies ; 
and  the  other  that  which  I  have  endeavoured  to 
demonstrate,  and  of  which  I  have  the  reputation  of 
being  the  author,  though  others  have  had  nearly  the 
same  ideas  of  it.  Perhaps  I  may  have  succeeded 
better  than  they  in  carrying  it  to  a  higher  degree 
of  evidence.  It  will  be  of  importance,  then,  to  show, 
tn  both  systems,  on  what  principle  the  difference  of 
colours  may  be  established. 

In  that  of  emanation,  which  supposes  the  rays  to 
issue  from  luminous  bodies,  in  the  form  of  rivers,  or 
rather  of  fountains,  spouting  out  a  fluid  in  all  direc- 
tions, it  is  alleged  that  the  particles  of  light  differ  in 
size  or  in  substance,  as  a  fountain  might  emit  wine, 
oil,  and  other  liquids ;  so  that  the  different  colours 
are  occasioned  by  the  diversity  of  the  subtile  matter 
which  emanates  from  luminous  bodies.  Red  would 
be,  accordingly,  a  subtile  matter  issuing  from  the 
luminous  body,  and  so  of  yellow  and  the  other 
colours.  This  explanation  would  exhibit  clearly 
enough  the  origin  of  the  different  colours,  if  the  sys- 
tem itself  had  a  solid  foundation.  I  shall  enter  into 
the  subject  more  at  large  in  my  next  Letter, 

2d  June,  176L 


08  THE    ANALOGY    BETWEEN 

LETTER  XIX. 

Reflections  on  the  Analogy  between  Colours  and  Sounds 

You  will  be  pleased  to  recollect  the  objections  I 
offered  to  the  system  of  the  emanation  of  light.* 
They  appear  to  me  so  powerful  as  completely  to 
overturn  that  system.  I  have  accordingly  succeeded 
in  my  endeavours  to  convince  certain  natural  phi- 
losophers of  distinction,  and  they  have  embraced  my 
sentiments  of  the  subject  with  expressions  of  singu- 
lar satisfaction. 

Rays  of  light,  then,  are  not  an  emanation  from 
the  sun  and  other  luminous  bodies,  and  do  not  con- 
sist of  a  subtile  matter  emitted  forcibly  by  the  sun, 
and  transmitted  to  us  with  a  rapidity  which  may  well 
fill  you  with  astonishment.  If  the  rays  employed 
only  eight  minutes  in  their  course  from  the  sun  to 
us,  the  torrent  would  be  terrible,!  and  the  mass  of 
that  luminary,  however  vast,  must  speedily  be  ex- 
hausted. 

According  to  my  system,  the  rays  of  the  sun,  of 
which  we  have  a  sensible  perception,  do  not  proceed 
immediately  from  that  luminary;  they  are  only  par- 
ticles of  ether  floating  around  us,  to  which  the  sun 
communicates  nearer  and  nearer  a  motion  of  vibra- 
tion, and  consequently  they  do  not  greatly  change 
their  place  in  this  motion. 

This  propagation  of  light  is  performed  m  a  manner 
similar  to  that  of  sound.  A  bell,  whose  sound  you 
hear,  by  no  means  emits  the  particles  which  enter 
your  ears.  You  have  only  to  touch  it  when  struck 
to  be  assured  that  all  its  parts  are  in  a  very  sensible 

!  *  See  Letters  XVT1.  and  XVIIf.  in  vol.  i. 

•  t  The  rapidity  of  the  progress  of  light,  if  it  be  objectionable  on  the 
theory  of  emanation,  must  be  equally  so  on  that  of  undulation  ;  for  the 
velocity  is  a  fact  derived  from  observation,  and  is  independent  of  theory, 
—Am,  Ed. 


COLOURS    AND    SOUNDS.  69 

agitation.  This  agitation  immediately  communicates 
itself  to  the  more  remote  particles  of  air,  so  that  all 
receive  from  it  successively  a  similar  motion  of  vi- 
bration, which,  reaching  the  ear,  excite  in  it  the  sen- 
sation of  sound.  The  strings  of  a  musical  instru- 
ment put  the  matter  beyond  all  doubt ;  you  see  them 
tremble,  go  and  come.  It  is  even  possible  to  deter- 
termine  by  calculation  how  often  in  a  second  each 
string  vibrates  ;  and  this  agitation,  being  communi- 
cated to  the  particles  of  air  adjacent  to  the  organ 
of  hearing,  the  ear  is  struck  by  it  precisely  as  often 
in  a  second.  It  is  the  perception  of  this  tremulous 
agitation  which  constitutes  the  nature  of  sound. 
The  greater  the  number  of  vibrations  produced  by 
the  string  in  a  second,  the  higher  or  sharper  is 
the  sound.  Vibrations  less  frequent  produce  lower 
notes. 

We  find  the  circumstances  which  accompany  the 
sensation  of  hearing,  in  a  manner  perfectly  analogous, 
in  that  of  sight. 

The  medium  only  and  the  rapidity  of  the  vibra- 
tions differ.  In  sound,  it  is  the  air  through  which 
the  vibrations  of  sonorous  bodies  are  transmitted. 
But  with  respect  to  light,  it  is  the  ether,  or  that  me- 
dium incomparably  more  subtile  and  more  elastic 
than  air,  which  is  universally  diffused  wherever  the 
air  and  grosser  bodies  leave  interstices. 

As  often,  then,  as  this  ether  is  put  into  a  state  of 
vibration,  and  is  transmitted  to  the  eye,  it  excites 
in  it  the  sentiment  of  vision,  which  is  in  that  case 
nothing  but  a  similar  tremulous  motion,  whereby 
the  small  nervous  fibres  at  the  bottom  of  the  eye 
are  agitated. 

You  easily  comprehend  that  the  sensation  must 
be  different,  according  as  this  tremulous  agitation  is 
more  or  less  frequent ;  or  according  as  the  number 
of  vibrations  performed  in  a  second  is  greater  or 
less.  Hence  there  must  result  a  difference  similar 
to  that  which  takes  place  in  sounds,  when  the  vibra- 


70  THE    ANALOGY    BETWEEN 

tions  are  more  or  less  frequent.  This  difference  is 
clearly  perceptible  by  the  ear,  as  the  character  of 
sounds  in  respect  of  flat  and  sharp  depends  on  it. 
You  will  recollect  that  the  note  marked  C  in  the 
harpsichord  performs  about  100  vibrations  in  a  sec- 
ond, note  D  112,  note  E  125,  note  F  133,  note  G  150, 
note  A  166,  note  B  187,  and  200.  Thus  the  nature 
of  sounds  depends  on  the  number  of  vibrations  per- 
formed in  a  second. 

It  cannot  be  doubted  that  the  sense  of  seeing  may 
be  likewise  differently  affected,  according  as  the 
number  of  vibrations  of  the  nervous  fibres  of  the 
bottom  of  the  eye  is  greater  or  less.  When  these 
fibres  vibrate  1000  times  in  a  second,  the  sensation 
must  be  quite  different  from  what  it  would  be  did 
they  vibrate  1200  or  1500  times  in  the  same  space. 

True  it  is  that  the  organ  of  vision  is  not  in  a  con- 
dition to  reckon  numbers  so  great,  still  less  than  the 
ear  is  to  reckon  the  vibrations  which  constitute 
sound  ;  but  it  is  always  in  our  power  to  distinguish 
between  the  greater  and  the  less. 

In  this  difference,  therefore,  we  must  look  for  the 
cause  of  difference  of  colour ;  and  it  is  certain  that 
each  of  them  corresponds  to  a  certain  number  of 
vibrations,  by  which  the  fibres  of  our  eyes  are  struck 
in  a  second,  though  we  are  not  as  yet  in  a  condition 
to  determine  the  number  corresponding  to  each  par- 
ticular colour,  as  we  can  do  with  respect  to  sounds. 

Much  research  must  have  been  employed  before 
it  was  possible  to  ascertain  the  numbers  correspond- 
ing to  all  the  notes  of  the  harpsichord,  though  there 
was  an  antecedent  conviction  that  their  difference 
was  founded  on  the  diversity  of  those  numbers.  Our 
knowledge  respecting  these  objects  is  nevertheless 
considerably  advanced,  from  our  being  assured  that 
there  prevails  a  harmony  so  delightful  between  the 
different  notes  of  the  harpsichord  and  the  different 
colours  ;  and  that  the  circumstances  of  the  one  serve 
to  elucidate  those  of  the  other.  This  analogy  ao*. 


COLOURS    AND    SOUNDS.  71 

eordingly  furnishes  the  most  convincing  proofs  in 
support  of  my  system.  But  I  have  reasons  still 
more  solid  to  adduce,  which  will  secure  it  from  every 
attack. 

bthJune,  1761, 


LETTER  xxk 

Continuation. 

NOTHING  is  more  adapted  to  the  communication 
Of  knowledge  respecting  the  nature  of  vision  than 
the  analogy  discoverable,  almost  in  every  particular, 
between  it  and  the  hearing.  Colours  are  to  the  eye 
what  sounds  are  to  the  ear.  They  differ  from  each 
other  as  flat  and  sharp  notes  differ.  ]N"ow  we  know 
that  flat  and  sharp  in  sounds  depends  on  the  number 
of  vibrations  whereby  the  organ  of  hearing  is  struck 
in  a  given  time,  and  that  the  nature  of  each  is  deter- 
mined by  a  certain  number,  which  marks  the  vibra- 
tions performed  in  a  second.  From  this  I  conclude 
that  each  colour  is  likewise  restricted  to  a  number 
of  vibrations  which  act  on  vision ;  with  this  differ- 
ence, that  the  vibrations  which  produce  sound  reside 
in  gross  air,  whereas  those  of  light  and  colours  are 
transmitted  through  a  medium  incomparably  more 
subtile  and  elastic.  The  same  thing  holds  as  to  the 
objects  of  both  senses.  Those  of  hearing  are  all 
of  them  bodies  adapted  to  the  transmission  of  sound, 
that  is,  susceptible  of  a  motion  of  vibration,  or  of  a 
tremulous  agitation,  which,  communicating  itself  to 
the  air,  excites  in  the  organ  the  sensation  of  a  sound 
corresponding  to  the  rapidity  of  the  vibrations. 

Such  are  all  musical  instruments ;  and  to  confine 
myself  principally  to  the  harpsichord,  we  ascribe  to 
each  string  a  certain  sound  which  it  produces  when 
struck.  Thus,  one  string  is  named  C,  another  D, 
and  so  on.  A  string  is  named  C  when  its  structure 


72       ANALOGY  BETWEEN  COLOURS   AND  SOUNDS, 

and  tension  are  such  that,  being  struck,  it  produces 
about  100  vibrations  in  a  second  ;  and  if  it  produced 
less  or  more  in  the  same  time,  it  would  have  the 
name  of  a  different  note,  higher  or  lower. 

You  will  please  to  recollect  that  the  sound  of  a 
string  depends  on  three  things — its  length,  its  thick- 
ness, and  the  degree  of  tension ;  the  more  it  is 
stretched  the  sharper  its  sound  becomes ;  and  as 
long  as  it  preserves  the  same  disposition,  it  emits 
the  same  sound ;  but  that  changes  as  soon  as  the 
other  undergoes  any  variation. 

Let  us  apply  this  to  bodies  which  are  the  objects 
of  vision.  The  minuter  particles  which  compose 
the  tissue  of  their  surface  may  be  considered  as 
strings  distended,  in  as  much  as  they  are  endowed 
with  a  certain  degree  of  elasticity  and  bulk,  so  that, 
being  struck,  they  acquire  a  motion  of  vibration,  of 
which  they  will  finish  a  certain  number  in  a  second; 
and  on  this  number  depends  the  colour  which  we 
ascribe  to  such  body.  It  is  red  when  the  particles 
of  its  surface  have  such  a  degree  of  tension  that, 
being  agitated,  they  perform  precisely  so  many  vi- 
brations in  a  second  as  are  necessary  to  excite  in  us 
the  sensation  of  that  colour.  A  degree  of  tension 
which  would  produce  vibrations  more  or  less  rapid 
would  excite  that  of  a  different  colour,  and  then  the 
body  would  be  yellow,  green,  or  blue,  &c. 

We  have  not  as  yet  acquired  the  ability  of  assign- 
ing to  each  colour  the  number  of  vibrations  which 
constitute  its  essence  ;  we  do  not  so  much  as  know 
which  are  the  colours  that  require  a  greater  or  less 
rapidity  of  vibration,  or  rather,  it  is  not  yet  deter- 
mined what  colours  correspond  with  high  or  low 
notes.  It  is  sufficient  to  know  that  each  colour  is 
attached  to  a  certain  number  of  vibrations,  though  it 
has  not  hitherto  been  ascertained  ;  and  that  you  have 
only  to  change  the  tension  of  elasticity  of  the  par- 
ticles which  form  the  surface  of  a  body,  to  make  it 
change  colour. 


OPAQUE    BODIES    RENDERED    VISIBLE.  73 

We  see  that  the  most  beautiful  colours  in  flowers 
quickly  change  and  disappear,  from  a  failure  of  the 
nutritive  juices ;  and  because  their  particles  lose 
their  vigour  or  their  tension.  This,  too,  is  observa- 
ble in  every  other  change  of  colour. 

To  place  this  in  a  clearer  light,  let  us  suppose  that 
the  sensation  of  red  requires  such  a  rapidity  of  vibra- 
tion, that  1000  are  performed  in  a  second  ;  that 
orange  requires  1125,  yellow  1250,  green  1333,  blue 
1500,  and  violet  1666.  Though  these  numbers  are 
only  supposed,  this  does  not  affect  the  object  I  have 
in  view.  What  I  say  as  to  these  numbers  will  apply 
in  like  manner  to  the  really  corresponding  numbers, 
if  ever  they  are  discovered. 

A  body,  then,  will  be  red  when  the  particles  of  its 
surface,  put  in  vibration,  complete  1000  in  a  second ; 
another  body  will  be  orange  when  disposed  so  as  to 
complete  1 125  in  a  second,  and  so  on.  Hence  it  is 
obvious  that  there  must  be  an  endless  variety  of  in- 
termediate colours  between  the  six  principal  which 
I  have  mentioned  ;  and  it  is  likewise  evident,  if  the 
particles  of  a  body,  being  agitated,  should  perform 
1400  vibrations  in  a  second,  it  would  be  of  an  inter- 
mediate colour  between  green  and  blue  ;  green  cor- 
responding to  number  1333,  and  blue  to  1500. 

QthJune,  1761. 


LETTER  XXI. 

How  Opaque  Bodies  are  rendered  visible. 

You  will  find  no  difficulty  in  the  definition  I 
have  been  giving  of  coloured  bodies.  The  particles 
of  their  surface  are  always  endowed  with  a  certain 
degree  of  elasticity,  which  renders  them  suscep- 
tible of  a  motion  of  vibration,  as  a  string  is  always 
susceptible  of  a  certain  sound  ;  and  it  is  the  number 
of  vibrations  which  these  particles  are  capable  of 

VOL.  II.— G 


74  OPAQUE    BODIES    RENDERED    VISIBLE. 

making  in  a  second  which  determines  the  species 
of  colour. 

If  the  particles  of  the  surface  have  not  elasticity 
sufficient  to  admit  of  such  agitation,  the  body  must 
be  black,  this  colour  being  nothing  else  but  a  depri- 
vation of  light,  and  all  bodies  from  which  no  rays 
are  transmitted  to  our  eyes  appearing  black. 

I  now  come  to  a  very  important  question,  re- 
specting which  some  doubts  may  be  entertained.  It 
may  be  asked,  What  is  the  cause  of  the  motion  of 
vibration  which  constitutes  the  colours  of  bodies  ? 

Into  the  discovery  of  this,  indeed,  the  whole  is 
resolved  ;  for  as  soon  as  the  particles  of  bodies  shall 
be  put  in  motion,  the  ether  diffused  through  the  air 
will  immediately  receive  a  similar  agitation,  which, 
continued  to  our  eyes,  constitutes  there  that  which 
we  call  rays,  from  which  vision  proceeds. 

I  remark,  first,  that  the  particles  of  bodies  are  not 
put  in  motion  by  an  internal,  but  an  external  power, 
just  as  a  string  distended  would  remain  for  ever  at 
rest,  were  it  not  put  in  motion  by  some  external 
force.  Such  is  the  case  of  all  bodies  in  the  dark ; 
for,  as  we  see  them  not,  it  is  a  certain  proof  that 
they  emit  no  rays,  and  that  their  particles  are  at  rest. 
In  other  words,  during  the  night  bodies  are  in  the 
same  state  with  the  strings  of  an  instrument  that  is 
not  touched,  and  which  emit  no  sound;  whereas 
bodies  rendered  visible  may  be  compared  to  strings 
which  emit  sound. 

And  as  bodies  become  visible  as  soon  as  they  are 
illuminated,  that  is,  as  soon  as  the  rays  of  the  sun, 
or  of  some  other  luminous  body,  fall  upon  them,  it 
must  follow,  that  the  same  cause  which  illuminates 
them  must  excite  their  particles  to  generate  rays, 
and  to  produce  in  our  eyes  the  sensation  of  vision. 
The  rays  of  light,  then,  falling  upon  a  body,  put  its 
particles  into  a  state  of  vibration. 

This  appears  at  first  surprising,  because  on  ex- 
posing our  hands  to  the  strongest  light  no  sensible 


OPAQUE    BODIES    RENDERED   VISIBLE.  75 

impression  is  made  on  them.  It  is  to  be  considered, 
that  the  sense  of  touch  is  in  us  too  gross  to  perceive 
these  subtile  and  slight  impressions ;  but  that  the 
sense  of  sight,  incomparably  more  delicate,  is 
powerfully  affected  by  them.  This  furnishes  an  in- 
contestable proof  that  the  rays  of  light  which  fall 
upon  a  body  possess  sufficient  force  to  act  upon  the 
minuter  particles,  and  to  communicate  to  them  a 
tremulous  agitation.  And  in  this  precisely  consists 
the  action  necessary  to  explain  how  bodies,  when 
illuminated,  are  put  in  a  condition  themselves  to 
produce  rays,  by  means  of  which  they  become 
visible  to  us.  It  is  sufficient  that  bodies  should  be 
luminous  or  exposed  to  the  light,  in  order  to  the 
agitation  of  their  particles,  and  thereby  to  their 
producing  themselves  rays  which  render  them  visible 
to  us. 

The  perfect  analogy  between  hearing  and  sight 
gives  to  this  explanation  the  highest  degree  of  prob- 
ability. Let  a  harpsichord  be  exposed  to  a  great 
noise,  and  you  will  see  that  not  only  the  strings  in 
general  are  put  into  a  state  of  vibration,  but  you 
will  hear  the  sound  of  each,  almost  as  if  it  were 
actually  touched.  The  mechanism  of  this  phenome- 
non is  easily  comprehended,  as  soon  as  it  is  known 
that  a  string  agitated  is  capable  of  communicating 
to  the  air  the  same  motion  of  vibration  which,  trans- 
mitted to  the  ear,  excites  in  it  the  sensation  of  the 
sound  which  thai  same  string  emits. 

Now,  as  a  string  produces  in  the  air  such  a  mo- 
tion, it  follows  that  the  air  reciprocally  acts  on  the 
string,  and  gives  it  a  tremulous  motion.  And  as  a 
noise  is  capable  of  putting  in  motion  the  strings  of 
a  harpsichord,  and  of  extracting  sounds  from  them, 
the  same  thing  must  take  place  in  the  objects  of 
vision. 

Coloured  bodies  are  similar  to  the  strings  of  a 
harpsichord,  and  the  different  colours  to  the  differ- 
ent notes,  in  respect  of  high  and  low.  The  light 


76  WONDERS    OF    THE    HUMAN   VOICE. 

which  falls  on  these  bodies,  being  analogous  to  the 
noise  to  which  the  harpsichord  is  exposed,  acts  on 
the  particles  of  their  surface  as  that  noise  acts  on 
the  strings  of  the  harpsichord  ;  and  these  particles 
thus  put  in  vibration  will  produce  the  rays  which 
shall  render  the  body  visible. 

This  elucidation  seems  to  me  sufficient  to  dissi- 
pate every  doubt  relating  to  my  theory  of  colours. 
I  flatter  myself,  at  least,  that  I  have  established  the 
true  principle  of  all  colours,  as  well  as  explained 
how  they  become  visible  to  us  only  by  the  light 
whereby  bodies  are  illuminated,  unless  such  doubts 
turn  upon  some  other  point  which  I  have  not 
touched  upon. 

13^  June,  1761. 


LETTER  XXII. 

The  Wonders  of  the  Human  Voice. 

IN  explaining  the  theory  of  sounds,  I  considered 
only  two  respects  in  which  sounds  could  differ :  the 
one  regarded  the  force  of  sound,  and  I  remarked 
that  it  is  greater  in  proportion  as  the  vibrations  ex- 
cited in  the  air  are  more  violent.  Thus,  the  noise 
of  a  discharge  of  cannon,  or  the  ringing  of  a  bell, 
has  more  force  than  that  of  a  string,  or  of  the  hu- 
man voice. 

The  other  difference  of  sounds  is  totally  inde- 
pendent of  this,  and  refers  to  flat  and  sharp,  accord- 
ing to  which  we  say  some  are  low  and  others  high. 
My  remark  relatively  to  this  difference  made  it  to 
depend  on  the  number  of  vibrations  completed  in  a 
certain  given  time,  say  a  second ;  so  that  the  greater 
such  number  is,  the  "higher  or  sharper  is  the  sound; 
and  the  smaller  it  is,  the  sound  is  lower  or  flatter. 

You  can  easily  comprehend  how  the  same  note 
may  be  either  strong  or  faint ;  accordingly,  we  see 


WONDERS    OF    THE    HUMAN   VOICE.  77 

that  the  forte  and  piano  employed  by  musicians 
change  in  no  respect  the  nature  of  sounds.  Among 
the  good  qualities  of  a  harpsichord,  it  is  required 
that  all  the  notes  should  have  nearly  the  same  de- 
gree of  strength ;  and  it  is  always  considered  as  a 
great  fault  when  some  of  the  strings  are  wound  up 
to  a  greater  degree  of  force  than  the  rest.  Now 
the  flat  and  the  sharp  are  referable  only  to  the  simple 
sounds,  whose  vibrations  follow  regularly,  and  at 
equal  intervals ;  and  in  music  we  employ  only  those 
sounds  which  are  denominated  simple.  Accords 
are  compound  sounds,  or  the  concourse  of  several 
produced  at  once,  among  the  vibrations  of  which  a 
certain  order  must  predominate,  which  is  the  found- 
ation of  harmony.  But  when  no  relation  among 
the  vibrations  is  perceptible,  it  is  a  confused  noise, 
with  which  it  is  impossible  to  say  what  note  of  the 
harpsichord  is  in  tune,  such  as  the  report  of  a  can- 
non or  musket. 

There  is  still  another  remarkable  difference  among 
the  simple  sounds,  which  seems  to  have  escaped 
the  attention  of  philosophers.  Two  sounds  may  be 
of  equal  force,  and  in  accord  with  the  same  note  of 
the  harpsichord,  and  yet  very  different  to  the  ear. 
The  sound  of  a  flute  is  totally  different  from  that  of 
the  French  horn,  though  both  may  be  in  tune  with 
the  same  note  of  the  harpsichord,  and  equally  strong; 
each  sound  derives  a  certain  peculiarity  from  the 
instrument  which  emits  it,  but  it  is  impossible  to 
describe  wherein  this  consists ;  the  same  string  too 
emits  different  sounds,  according  as  it  is  struck, 
touched,  or  pinched.  You  can  easily  distinguish  the 
sound  of  the  horn,  the  flute,  and  other  musical  in- 
struments. 

The  most  wonderful  diversity,  to  say  nothing  of 
the  variety  of  articulation  in  speech,  is  observable 
in  the  human  voice,  that  astonishing  masterpiece  of 
the  Creator.  Reflect  but  for  a  moment  on  the  dif- 
ferent vowels  which  the  mouth  simply  pronounces 
G2 


78  WONDERS    OF    THE    HUMAN   VOICE. 

or  sings.  When  the  vowel  a  is  pronounced  or  sung1, 
the  sound  is  quite  different  from  that  of  e,  i,  o,  u,  or 
ai  pronounced  or  sung,  though  on  the  same  tone. 
We  must  not  then  look  for  the  reason  of  this  differ- 
ence in  the  rapidity  or  order  of  the  vibrations ;  no 
investigation  of  philosophers  has  hitherto  unfolded 
this  mystery. 

You  must  be  perfectly  sensible,  that  in  order  to 
utter  these  different  vowels,  a  different  conformation 
must  be  given  to  the  cavity  of  the  mouth ;  and  that 
in  man  the  organization  of  this  part  is  much  better 
adapted  to  produce  these  effects  than  that  of  ani- 
mals. We  find,  accordingly,  that  certain  birds 
which  learn  to  imitate  the  human  voice  are  never 
capable  of  distinctly  pronouncing  the  different 
vowels ;  the  imitation  is  at  best  extremely  imperfect. 

In  many  organs  there  is  a  stop  which  bears  the 
name  of  the  human  voice ;  it  usually,  however, 
contains  only  the  notes  which  express  the  vocal 
sounds  ai  or  ae.  I  have  no  doubt,  that  with  some 
change  it  might  be  possible  to  produce  likewise  the 
other  vocal  sounds  a,  e,  »',  o,  w,  ou ;  but  even  this 
would  not  be  sufficient  to  imitate  a  single  word  of 
the  human  voice ;  for  how  can  we  combine  them 
with  the  consonants,  which  are  so  many  modifica- 
tions of  the  vowels  ?  We  are  so  conformed,  that 
however  common  the  practice,  it  is  almost  impos- 
sible to  trace  and  explain  the  real  mechanism. 

We  distinctly  observe  three  organs  employed  in 
expressing  the  consonants,  the  lips,  the  tongue,  and 
the  palate ;  but  the  nose  likewise  essentially  concurs. 
On  stopping  it,  we  become  incapable  of  pronouncing 
the  letters  m  and  n;  the  sound  of  b  and  d  only  is 
then  to  be  heard.  A  striking  proof  of  the  marvel- 
lous structure  of  our  mouth  for  the  pronunciation  of 
the  letters  undoubtedly  is,  that  all  the  skill  of  man 
has  not  hitherto  been  capable  of  producing  a  piece 
of  mechanism  that  could  imitate  it.  The  song  has 
">een  exactly  imitated,  but  without  any  articulation 


PHENOMENA    OF    ELECTRICITY.  79 

of  sounds,  and  without  distinction  of  the  different 
vowels. 

The  construction  of  a  machine  capable  of  express- 
ing sounds,  with  all  the  articulations,  would  no 
doubt  be  a  very  important  discovery.  Were  it  pos- 
sible to  execute  such  a  piece  of  mechanism,  and 
bring1  it  to  such  perfection  that  it  could  pronounce 
all  words,  by  means  of  certain  stops,  like  those  of 
an  organ  or  harpsichord,  every  one  would  be  sur- 
prised, and  justly,  to  hear  a  machine  pronounce 
whole  discourses  or  sermons  together,  with  the 
most  graceful  accompaniments.  Preachers  and 
other  orators,  whose  voice  is  either  too  weak  or 
disagreeable,  might  play  their  sermons  or  orations 
on  such  a  machine,  as  organists  do  pieces  of  music. 
The  thing  does  not  seem  to  me  impossible.* 

IQth  June,  1761. 


LETTER  XXIII. 

A  Summary  of  the  principal  Phenomena  of  Electricity. 

THE  subject  which  I  am  now  going  to  recommend 
to  your  attention  almost  terrifies  me.  The  variety 
it  presents  is  immense,  and  the  enumeration  of  facts 
serves  rather  to  confound  than  to  inform.  The  sub- 

*  Pipes  have  actually  been  constructed  of  such  forms,  by  Kratzen- 
stein  and  Kempelen,  as  to  imitate  very  accurately  the  different  vowel 
sounds  produced  by  the  human  voice.  From  this  first  attempt  Kempelen 
proceeded  to  analyze  the  mechanism  of  speech,  and  he  succeeded  in  con- 
structing a  speaking  machine,  which  uttered,  not  only  words,  but  entire 
sentences.  The  four  letters  D,  G,  K,  T,  however,  baffled  all  his  inge- 
nuity ;  and  lie  was  obliged  to  substitute  for  them  the  letter  P,  which  was 
so  managed  as  to  bear  a  considerable  resemblance  to  them,  so  much  so, 
at  least,  as  to  deceive  the  auditory. — See  the  Edinburgh,  Encyclopaedia, 
article  ACOUSTICS,  vol.  i.  p.  126;  and  AUTOMATON,  vol.  iii.  p.  153,  where 
a  full  account  of  this  machine  is  given.— Ed. 

The  ingenuity  of  the  Swiss  mechanicians  in  constructing  artificial 
birds,  dogs,  and  other  animals  which  emit  sounds  so  nearly  resembling 
those  of  their  prototypes  as  to  deceive  many  ears,  is  known  to  those  who 
have  visited  the  workshops  of  Geneva,  Locle,  Chande-lbnds  and  other 
towns.  See  on  this  subject  Brewster's  Natural  Magic,  No.  L.  Harper's 
Family  Library.— Am.  Ed. 


80  SUMMARY    OF   THE    PRINCIPAL 

ject  I  mean  is  electricity,  which  for  some  time  past 
has  become  an  object  of  such  importance  in  phy- 
sics that  every  one  is  supposed  to  be  acquainted 
with  its  effects. 

You  must  undoubtedly  have  frequently  heard  it 
mentioned  in  conversation  ;  but  I  know  not  whether 
you  have  ever  witnessed  any  of  the  experiments. 
Natural  philosophers  of  modern  times  prosecute  the 
study  of  it  with  ardour,  and  are  almost  every  day 
discovering;  new  phenomena,  the  description  of 
which  would  employ  many  hundreds  of  letters ;  nay, 
perhaps  I  should  never  have  done. 

And  here  it  is  I  am  embarrassed.  I  could  not 
bear  to  think  of  letting  you  remain  unacquainted 
with  a  branch  of  natural  philosophy  so  essential ; 
but  I  would  willingly  save  you  the  fatigue  of  wading 
through  a  diffuse  detail  of  the  phenomena,  which 
after  all  would  not  furnish  the  necessary  informa- 
tion. I  flatter  myself,  however,  that  I  nave  dis- 
covered a  road  which  will  lead  so  directly  to  the 
object,  that  you  shall  attain  a  knowledge  of  it  much 
more  perfect  than  that  of  most  natural  philosophers, 
who  devote  night  and  day  to  the  investigation  of 
these  mysteries  of  nature. 

Without  stopping  to  explain  the  various  appear- 
ances and  effects  of  electricity,  which  would  engage 
me  in  a  long  and  tedious  detail,  without  extending 
your  knowledge  of  the  causes  which  produce  these 
effects,  I  shall  pursue  quite  a  different  course,  and 
begin  with  unfolding  the  true  principle  of  nature  on 
which  all  these  phenomena  are  founded,  however 
various  they  may  appear,  and  from  which  they  are 
all  easily  deducible. 

It  is  sufficient  to  remark,  in  general,  that  elec- 
tricity is  excited  by  the  friction  of  a  glass  tube.  It 
thereby  becomes  electrical :  and  then  it  alternately 
attracts  and  repels  light  bodies  which  are  applied  to 
it ;  and  on  the  application  of  other  bodies,  sparks  of 
fire  are  mutually  extracted,  which,  increased  in 
strength,  kindle  spirits  of  wine  and  other  combustible 


PHENOMENA    OF    ELECTRICITY.  81 

substances.  On  touching  such  a  tube  with  the 
finger,  you  feel,  besides  the  spark,  a  puncture  which 
may  in  certain  circumstances  be  rendered  so  acute 
as  to  produce  a  commotion  through  the  whole  body. 

Instead  of  a  tube  of  glass,  we  likewise  employ  a 
globe  of  glass,  which  is  made  to  turn  round  an  axis 
like  a  turning- wheel.  During  this  motion  it  is  rubbed 
with  the  hand,  or  with  a  cushion  applied  to  it ;  then 
the  globe  becomes  electric,  and  produces  the  same 
phenomena  as  the  tube. 

Besides  glass,  resinous  bodies,  such  as  Spanish 
wax,  and  sulphur,  likewise  possess  the  property  of 
becoming  electric  by  friction;  but  certain  species 
of  bodies  only  have  this  quality,  of  which  glass, 
sealing-wax,  and  sulphur  are  the  principal. 

Other  bodies  undergo  friction  without  producing 
any  such  effect ;  no  sign  of  electricity  appears :  but 
on  applying  them  to  the  first,  when  rendered  elec- 
tric, they  immediately  acquire  the  same  property. 
They  become  electric,  then,  by  communication,  as 
they  touch ;  and  frequently  the  approximation  only 
of  electric  bodies  renders  them  such. 

All  bodies,  therefore,  are  divisible  into  two  classes ; 
in  the  one  are  included  those  that  become  electric  by 
friction,  in  the  other  those  which  are  rendered  such 
by  communication,  whereas  friction  produces  no 
manner  of  effect  on  them.  It  is  very  remarkable 
that  bodies  of  the  first  class  receive  no  electricity 
from  communication  ;  when  you  apply  to  a  tube  or 
globe  of  glass  strongly  electrified,  other  glasses  or 
bodies  which  friction  renders  electric,  this  touch 
communicates  no  electricity  to  them.  The  distinc- 
tion of  these  two  classes  of  bodies  is  worthy  of 
attention ;  the  one  class  being  disposed  to  become 
electrical  by  friction  only,  and  not  by  communica- 
tion— the  other,  on  the  contrary,  only  by  com- 
munication.* 

*  The  distinction  between  these  two  classes  is  not  so  absolute  as  the 
author's  remark  would  lead  the  student  to  infer.  The  classes  are,  with 
proper  precaution,  convertible  into  each  other.—  Am.  Ed. 


82  TRUE    PRINCIPLE    OF    NATURE, 

All  metals  belong  to  this  last  class,  and  the  com- 
munication extends  so  far,  that  on  presenting  one 
extremity  of  a  wire  to  an  electric  body,  the  other 
extremity  becomes  so  likewise,  be  the  wire  ever  so 
long ;  and  on  applying  still  another  wire  to  the  far- 
ther extremity  of  the  first,  the  electricity  is  conveyed 
through  the  whole  extent  of  that  second  thread — 
and  thus  electricity  may  be  transmitted  to  the  most 
remote  distances. 

Water  is  a  substance  which  receives  electricity  by 
communication.  Large  pools  have  been  electrified 
to  such  a  degree  that  the  application  of  the  finger 
has  elicited  sparks  and  excited  pain. 

The  prevailing  persuasion  now  is,  that  lightning 
and  thunder  are  the  effect  of  the  electricity  which 
the  clouds  acquire,  from  whatever  cause.  A  thunder- 
storm exhibits  the  same  phenomena  of  electricity, 
on  the  great  scale,  which  the  experiments  of  natural 
philosophers  do  in  miniature. 

20th  June,  1761. 


LETTER  XXIV. 

The  true  Principle  of  Nature  on  which  are  founded  all 
the  Phenomena  of  Electricity. 

THE  summary  I  have  exhibited  of  the  principal 
phenomena  of  electricity  has  no  doubt  excited  a 
cu-riosity  to  know  what  occult  powers  of  nature  are 
capable  of  producing  effects  so  surprising. 

The  greatest  part  of  natural  philosophers  acknow- 
ledge their  ignorance  in  this  respect.  They  appear 
to  be  so  dazzled  by  the  endless  variety  of  phenomena 
which  every  day  present  themselves,  and  by  the  sin-r 
gularly  marvellous  circumstances  which  accompany 
these  phenomena,  that  they  are  discouraged  from 
attempting  an  investigation  of  the  true  cause  of 
them.  They  readily  admit  the  existence  of  a  subtile 


ON    WHICH    ELECTRICITY   IS    FOUNDED.  83 

matter,  which  is  the  primary  agent  in  the  production 
of  the  phenomena,  and  which  they  denominate  the 
electric  fluid;  but  they  are  so  embarrassed  about 
determining  its  nature  and  properties,  that  this  im- 
portant branch  of  physics  is  rendered  only  more 
perplexed  by  their  researches. 

There  is  no  room  to  doubt  that  we  must  look  for 
the  source  of  all  the  phenomena  of  electricity  only 
in  a  certain  fluid  and  subtile  matter ;  but  we  have  no 
need  to  go  to  the  regions  of  imagination  in  quest  of 
it.  That  subtile  matter  denominated  ether,  whose 
reality  I  have  already  endeavoured  to  demonstrate,* 
is  sufficient  very  naturally  to  explain  all  the  sur- 
prising effects  which  electricity  presents.  I  hope  I 
shall  be  able  to  set  this  in  so  clear  a  light,  that  you 
shall  be  able  to  account  for  every  electrical  phe- 
nomenon, however  strange  an  appearance  it  may 
assume. 

The  great  requisite  is  to  have  a  thorough  know- 
ledge of  the  nature  of  ether.  The  air  which  we 
breathe  rises  only  to  a  certain  height  above  the  sur- 
face of  the  earth  ;  the  higher  you  ascend  the  more 
subtile  it  becomes,  and  at  last  it  entirely  ceases. 
We  must  not  affirm  that  beyond  the  region  of  the 
air  there  is  a  perfect  vacuum  which  occupies  the  im- 
mense space  in  which  the  heavenly  bodies  revolve. 
The  rays  of  light,  which  are  diffused  in  all  directions 
from  these  heavenly  bodies,  sufficiently  demonstrate 
that  those  vast  spaces  are  filled  with  a  subtile  matter. 

If  the  rays  of  light  are  emanations  forcibly  pro- 
jected from  luminous  bodies,  as  some  philosophers 
have  maintained,  it  must  follow  that  the  whole 
space  of  the  heavens  is  filled  with  these  rays — nay, 
that  they  move  through  it  with  incredible  rapidity. 
You  have  only  to  recollect  the  prodigious  velocity 
with  which  the  rays  of  the  sun  are  transmitted  to  us. 
On  this  hypothesis,  not  only  would  there  be  no 

*  See  Letter  XV.  vol.  1. 


84  PHENOMENA    OF    ELECTRICITY. 

vacuum,  but  all  space  would  be  filled  with  a  subtile 
matter,  and  that  in  a  state  of  constant  and  most 
dreadful  agitation. 

But  I  think  I  have  clearly  proved  that  rays  of 
light  are  no  more  emanations  projected  from  lumi- 
nous bodies  than  sound  is  from  sonorous  bodies. 
It  is  much  more  certain  that  rays  of  light  are  no- 
thing else  but  a  tremulous  motion  or  agitation  of  a 
subtile  matter,  just  as  sound  consists  of  a  similar 
agitation  excited  in  the  air.  And  as  sound  is  pro- 
duced and  transmitted  by  the  air,  light  is  produced 
and  transmitted  by  that  matter,  incomparably  more 
subtile,  denominated  ether,  which  consequently  fills 
the  immense  space  between  the  heavenly  bodies. 

Ether,  then,  is  a  medium  proper  for  the  transmis- 
sion of  rays  of  light :  and  this  same  quality  puts  us 
in  a  condition  to  extend  our  knowledge  of  "its  nature 
and  properties.  We  have  only  to  reflect  on  the 
properties  of  air,  which  render  it  adapted  to  the  re- 
ception and  transmission  of  sound.  The  principal 
cause  is  its  elasticity  or  spring.  You  know  that  air 
has  a  power  of  expanding  itself  in  all  directions,  and 
that  it  does  expand  the  instant  that  obstacles  are 
removed.  The  air  is  never  at  rest  but  when  its 
elasticity  is  everywhere  the  same ;  whenever  it  is 
greater  in  one  place  than  another  the  air  imme- 
diately expands.  We  likewise  discover  by  experi- 
ment that  the  more  the  air  is  compressed,  the  more 
its  elasticity  increases :  hence  the  force  of  air-guns, 
in  which  the  air,  being  very  strongly  compressed,  is 
capable  of  discharging  the  ball  with  astonishing  ve- 
locity. The  contrary  takes  place  when  the  air  is 
rarefied :  its  elasticity  becomes  less  in  proportion 
as  it  is  more  rarefied,  or  diffused  over  a  larger  spac^. 

On  the  elasticity  of  the  air,  then,  relative  to  its 
density,  depends  the  velocity  of  sound,  which  makes 
a  progress  of  1 142  feet  in  a  second.  If  the  elasticity 
of  the  air  were  increased,  its  density  remaining  the 
same,  the  velocity  of  sound  would  increase  ;  and  the 


DIFFERENT   NATURE    OF    BODIES.  85 

same  thing  would  take  place  if  the  air  were  more 
rare  or  less  dense  than  it  is,  its  elasticity  being  the 
same.  In  general,  the  mere  that  any  medium,  simi- 
lar to  air,  is  elastic,  and  at  the  same  time  less  dense, 
the  more  rapidly  will  the  agitations  excited  in  it  be 
transmitted.  And  as  light  is  transmitted  so  many 
thousand  times  more  rapidly  than  sound,  it  must 
clearly  follow  that  the  ether,  that  medium  whose 
agitations  constitute  light,  is  many  thousand  times 
more  elastic  than  air,  and,  at  the  same  time,  many 
thousand  times  more  rare  or  more  subtile,  both  of 
these  qualities  contributing  to  accelerate  the  propa- 
gation of  light. 

Such  are  the  reasons  which  lead  us  to  conclude 
that  ether  is  many  thousand  times  more  elastic  and 
more  subtile  than  air ;  its  nature  being  in  other  re- 
spects similar  to  that  of  air,  in  as  much  as  it  is  like- 
wise a  fluid  matter,  and  susceptible  of  compression 
and  of  rarefaction.  It  is  this  quality  which  will 
conduct  us  to  the  explanation  of  all  the  phenomena 
of  electricity. 

23d  June,  1761. 


LETTER  XXV. 

Continuation.     Different  Nature  of  Bodies  relatively 
to  Electricity. 

ETHER  being  a  subtile  matter  and  similar  to  air, 
but  many  thousand  times  more  rare  and  more 
elastic,  it  cannot  be  at  rest,  unless  its  elasticity,  or 
the  force  with  which  it  tends  to  expand,  be  the  same 
everywhere. 

As  soon  as  the  ether  in  one  place  shall  be  more 
elastic  than  in  another,  which  is  the  case  when  it  is 
more  compressed  there,  it  will  expand  itself  into  the 
parts  adjacent,  compressing  what  it  finds  there  till 
the  whole  is  reduced  to  the  same  degree  of  elasticity. 

VOL.  II.— H 


86  DIFFERENT    NATURE    OF    BODIES 

It  is  then  in  equilibrio,  the  equilibrium  being  nothing 
else  but  the  state  of  rest,  when  the  powers  which  have 
a  tendency  to  disturb  it  counterbalance  each  other. 

When,  therefore,  the  ether  is  not  in  equilibrio  the 
same  thing  must  take  place  as  in  air,  when  its  equi- 
librium is  disturbed ;  it  must  expand  itself  from  the 
place  where  its  elasticity  is  greater  towards  that 
where  it  is  less ;  but,  considering  its  greater  elasticity 
and  subtilty,  this  motion  must  be  much  more  rapid 
than  that  of  air.  The  want  of  equilibrium  in  the 
air  produces  wind,  or  the  motion  of  that  fluid  from 
one  place  to  another.  There  must  therefore  be  pro- 
duced a  species  of  wind,  but  incomparably  more 
subtile  than  that  of  air,  when  the  equilibrium  of  the 
ether  is  disturbed,  by  which  this  last  fluid  will  pass 
from  places  where  it  was  more  compressed  and 
more  elastic  to  those  where  it  was  less  so. 

This  being  laid  down,  I  with  confidence  affirm  that 
all  the  phenomena  of  electricity  are  a  natural  con- 
sequence of  want  of  equilibrium  in  the  ether,  so  that 
wherever  the  equilibrium  of  the  ether  is  disturbed 
the  phenomena  of  electricity  must  take  place  ;  con- 
sequently, electricity  is  nothing  else  but  a  derange- 
ment of  the  equilibrium  of  the  ether. 

In  order  to  unfold  all  the  effects  of  electricity,  we 
must  attend  to  the  manner  in  which  ether  is  blended 
and  enveloped  with  all  the  bodies  which  surround  us. 
Ether,  in  these  lower  regions,  is  to  be  found  only  in 
the  small  interstices  which  the  particles  of  the  air 
and  of  other  bodies  leave  unoccupied.  Nothing  can 
be  more  natural  than  that  the  ether,  from  its  extreme 
subtility  and  elasticity,  should  insinuate  itself  into 
the  smallest  pores  of  bodies  which  are  impervious 
to  air,  and  even  into  those  of  the  air  itself.  You  will 
recollect  that  all  bodies,  however  solid  they  may 
appear,  are  full  of  pores ;  and  many  experiments  in- 
contestably  demonstrate  that  these  interstices  occupy 
much  more  space  than  the  solid  parts ;  finally,  the 
less  ponderous  a  body  is,  the  more  it  must  be  filled 


RELATIVELY    TO    ELECTRICITY.  87 

with  these  pores,  which  contain  ether  only.  It  is 
clear,  therefore,  that  though  the  ether  he  thus  dif- 
fused through  the  smallest  pores  of  bodies,  it  must 
however  be  found  in  very  great  abundance  in  the 
vicinity  of  the  earth. 

You  will  easily  comprehend  that  the  difference  of 
these  pores  must  be  very  great,  both  as  to  magnitude 
and  figure,  according  to  the  different  nature  of  the 
bodies,  as  their  diversity  probably  depends  on  the 
diversity  of  their  pores.  There  must  be,  therefore, 
undoubtedly,  pores  more  close,  and  which  have  less 
communication  with  others ;  so  that  the  ether  which 
they  contain  is  likewise  more  confined,  and  cannot 
disengage  itself  but  with  great  difficulty,  though  its 
elasticity  may  be  much  greater  than  that  of  the 
ether  which  is  lodged  in  the  adjoining  pores.  There 
must  be,  on  the  contrary,  pores  abundantly  open, 
and  of  easy  communication  with  the  adjacent  pores ; 
in  this  case  it  is  evident  that  the  ether  lodged  in 
them  can  with  less  difficulty  disengage  itself  than 
in  the  preceding ;  and  if  it  is  more  or  less  elastic  in 
these  than  in  the  others,  it  will  soon  recover  its 
equilibrium. 

In  order  to  distinguish  these  two  classes  of  pores, 
I  shall  denominate  the  first  dose,  and  the  others 
open.  Most  bodies  must  contain  pores  of  an  inter- 
mediate species,  which  it  will  be  sufficient  to  dis- 
tinguish by  the  terms  more  or  less  close,  and  more  or 
less  open. 

This  being  laid  down,  I  remark,  first,  that  if  all 
bodies  had  pores  perfectly  close,  it  would  be  impos- 
sible to  change  the  elasticity  of  the  air  contained  in 
them ;  and  even  though  the  ether  in  some  of  these 
pores  should  have  acquired,  from  whatever  cause,  a 
higher  degree  of  elasticity  than  the  others,  it  would 
always  remain  in  that  state,  and  never  recover  its 
equilibrium,  from  a  total  want  of  communication. 
In  this  case  no  change  could  take  place  in  bodies ; 
all  would  remain  in  the  same  state  as  if  the  ether 


88  DIFFERENT   NATURE    OF    BODIES 

were  in  equilibrio,  and  no  phenomenon  of  electricity 
could  be  produced. 

This  would  likewise  be  the  case  if  the  pores  of 
all  bodies  were  perfectly  open ;  for  then,  though  the 
ether  might  be  more  or  less  elastic  in  some  pores 
than  in  others,  the  equilibrium  would  be  instantly 
restored,  from  the  entire  freedom  of  communication 
—and  that  so  rapidly  that  we  should  not  be  in  a 
condition  to  remark  the  slightest  change.  For  the 
same  reason  it  would  be  impossible  to  disturb  the 
equilibrium  of  the  ether  contained  in  such  pores ;  as 
often  as  the  equilibrium  might  be  disturbed,  it  would 
be  as  instantaneously  restored,  and  no  sign  of  elec- 
tricity would  be  discoverable. 

The  pores  of  all  bodies  being  neither  perfectly 
close  nor  perfectly  open,  it  will  always  be  possible 
to  disturb  the  equilibrium  of  the  ether  which  they 
contain :  and  when  this  happens,  from  whatever 
cause,  the  equilibrium  cannot  fail  to  re-establish 
itself;  but  this  re-establishment  will  require  some 
time,  and  this  produces  certain  phenomena;  and 
you  will  presently  see,  much  to  your  satisfaction, 
that  they  are  precisely  the  same  which  electrical 
experiments  have  discovered.  It  will  then  appear 
that  the  principles  on  which  I  am  going  to  establish 
the  theory  of  electricity  are  extremely  simple,  and 
at  the  same  time  absolutely  incontrovertible. 

27th  June,  1761. 


LETTER  XXVI. 

On  the  same  Subject. 

I  HOPE  I  have  now  surmounted  the  most  formi- 
dable difficulties  which  present  themselves  in  the 
theory  of  electricity.  You  have  only  to  preserve 
the  idea  of  ether  which  I  have  been  explaining ;  and 
which  is,  that  extremely  subtile  and  elastic  matter 


RELATIVELY    TO    ELECTRICITY.  89 

diffused,  not  only  through  all  the  void  spaces  of  the 
universe,  but  through  the  minutest  pores  of  all 
bodies  in  which  it  is  sometimes  more  and  sometimes 
less  engaged,  according  as  they  are  more  or  less 
close.  This  consideration  conducts  us  to  two  prin- 
cipal species  of  bodies,  of  which  the  one  has  pores 
more  close,  and  the  other  pores  more  open. 

Should  it  happen,  therefore,  that  the  ether  con- 
tained in  the  pores  of  bodies  has  not  throughout  the 
same  degree  of  elasticity,  and  that  it  is  more  or  less 
compressed  in  some  than  in  others,  it  will  make  an 
effort  to  recover  its  equilibrium  ;  and  it  is  precisely 
from  this  that  the  phenomena  of  electricity  take 
their  rise,  which,  of  consequence,  will  be  varied  in 
proportion  as  the  pores  in  which  the  ether  is  lodged 
are  various,  and  grant  it  a  communication  more  or 
less  free  with  the  others. 

This  difference  in  the  pores  of  bodies  perfectly 
corresponds  to  that  which  the  first  phenomena  of 
electricity  have  made  us  to  remark  in  them,  by  which 
some  easily  become  electrical  by  communication,  or 
the  proximity  of  an  electrical  body,  whereas  others 
scarcely  undergo  any  change.  Hence  you  will  im- 
mediately infer  that  bodies  which  receive  electricity 
so  easily  by  communication  alone  are  those  whose 
pores  are  open ;  and  that  the  others,  which  are 
almost  insensible  to  electricity,  must  have  theirs 
close,  either  entirely  or  to  a  very  great  degree. 

It  is,  then,  by  the  phenomena  of  electricity  them- 
selves that  we  are  enabled  to  conclude  what  are 
the  bodies  whose  pores  are  close  or  open.  Respect- 
ing which  permit  me  to  suggest  the  following  elu- 
cidations. 

First,  the  air  which  we  breathe  has  its  pores 
almost  entirely  close ;  so  that  the  ether  which  it 
contains  cannot  disengage  itself  but  with  difficulty, 
and  must  find  equal  difficulty  in  attempting  to  pene- 
trate into  it.  Thus,  though  the  ether  diffused 
through  the  air  is  not  in  equilibrio  with  that  which 
H  2 


90  DIFFERENT    NATURE    OF    BODIES 

is  contained  in  other  bodies  where  it  is  more  or  less 
compressed,  the  re-establishment  of  its  equilibrium 
is  not  to  be  produced  without  extreme  difficulty; 
this  is  to  be  understood  of  dry  air,  humidity  being 
of  a  different  nature,  as  I  shall  presently  remark. 

Further,  we  must  rank  in  this  class  of  bodies  with 
close  pores,  glass,  pitch,  resinous  bodies,  sealing-wax, 
sulphur,  and  particularly  silk.  These  substances  have 
their  pores  so  very  close  that  it  is  with  extreme 
difficulty  the  ether  can  either  escape  from  or  pene- 
trate into  them. 

The  other  class,  that  of  bodies  whose  pores  are 
open,  contains,  first,  water  and  other  liquors,  whose 
nature  is  totally  different  from  that  of  air.  For  this 
reason,  when  air  becomes  humid  it  totally  changes 
its  nature  with  respect  to  electricity,  and  the  ether 
can  enter  or  escape  without  almost  any  difficulty. 
To  this  class  of  bodies  with  open  pores  likewise 
must  be  referred  those  of  animals,  and  all  metals. 

Other  bodies,  such  as  wood,  several  sorts  of  stones 
and  earths,  occupy  an  intermediate  state  between  the 
two  principal  species  which  I  have  just  mentioned ; 
and  the  ether  is  capable  of  entering  or  escaping 
with  more  or  less  facility,  according  to  the  nature 
of  each  species. 

After  these  elucidations  on  the  different  nature 
of  bodies  with  respect  to  the  ether  which  they  con- 
tain, you  will  see  with  much  satisfaction  how  all 
the  phenomena  of  electricity,  which  have  been  con- 
sidered as  so  many  prodigies,  flow  very  naturally 
from  them. 

All  depends,  then,  on  the  state  of  the  ether  dif- 
fused or  dispersed  through  the  pores  of  all  bodies, 
in  as  far  as  it  has  not  throughout  the  same  degree 
of  elasticity,  or  as  it  is  more  or  less  compressed  in 
some  than  in  others :  for  the  ether  not  being  then  in 
equilibrio  will  make  an  effort  to  recover  it.  It  will 
endeavour  to  disengage  itself  as  far  as  the  openness 
of  the  pores  will  permit  from  places  where  it  is  too 


RELATIVELY    TO    ELECTRICITY.  91 

much  compressed,  to  expand  itself  and  enter  into 
pores  where  there  is  less  compression,  till  it  is 
throughout  reduced  to  the  same  degree  of  com- 
pression and  elasticity,  and  is,  of  consequence,  in 
equilibrio. 

Lei  it  be  remarked,  that  when  the  ether  passes 
from  a  body  where  it  was  too  much  compressed  into 
another  where  it  is  less  so,  it  meets  with  great  ob- 
stacles in  the  air  which  separates  the  two  bodies  on 
account  of  the  pores  of  this  fluid,  which  are  almost 
entirely  close.  It  however  passes  through  the  air 
as  a  liquid  and  extremely  subtile  matter,  provided 
its  force  is  not  inferior,  or  the  interval  between  the 
bodies  too  great.  Now,  this  passage  of  the  ether 
being  very  much  impeded,  and  almost  entirely  pre- 
vented by  the  pores  of  the  air,  the  same  thing  will 
happen  to  it  as  to  air  forced  with  velocity  through 
small  apertures — a  hissing  sound  is  heard — which 
proves  that  this  fluid  is  then  put  into  an  agitation 
which  produces  such  a  sound. 

It  is,  therefore,  extremely  natural  that  the  ether, 
forced  to  penetrate  through  the  pores  of  the  air, 
should  likewise  receive  a  species  of  agitation.  You 
will  please  to  recollect,  that  as  agitation  of  the  air 
produces  sound,  a  similar  agitation  of  ether  produces 
light.  As  often,  then,  as  ether  escapes  from  one 
body  to  enter  into  another,  its  passage  through  the 
air  must  be  accompanied  with  light ;  which  appears 
sometimes  under  the  form  of  a  spark,  sometimes 
under  that  of  a  flash  of  lightning,  according  as  its 
quantity  is  more  or  less  considerable. 

Here,  then,  is  the  most  remarkable  circumstance 
which  accompanies  most  electrical  phenomena,  ex- 
plained to  a  demonstration,  on  the  principles  I  have 
laid  down.*  I  shall  now  enter  into  a  more  particular 

*  To  those  conversant  with  the  various  phenomena  of  electricity,  the 
author's  theory  of  close  and  open  pores,  and  of  the  different  degrees  of 
compression  of  his  supposed  ether,  will  be  deemed  to  fall  very  far  short 
of  a  demonstration.— Am.  Ed 


92  OF    POSITIVE    AND 

detail,  which  will  furnish  me  with  a  very  agreeable 
subject  for  some  following  Letters. 
30th  June,  1761. 


LETTER  XXVII. 

Of  Positive  and  Negative  Electricity.     Explanation  of 
the  Phenomenon  of  Attraction. 

You  will  easily  comprehend,  from  what  I  have 
above  advanced,  that  a  body  must  become  electrical 
whenever  the  ether  contained  in  its  pores  becomes 
more  or  less  elastic  than  that  which  is  lodged  in 
adjacent  bodies.  This  takes  place  when  a  greater 
quantity  of  ether  is  introduced  into  the  pores  of  such 
body,  or  when  part  of  the  ether  which  it  contained  is 
forced  out.  In  the  former  case,  the  ether  becomes 
more  compressed,  and  consequently  more  elastic  ;  in 
the  other,  it  becomes  rarer,  and  loses  its  elasticity. 
In  both  cases  it  is  no  longer  in  equilibrio  with  that 
which  is  external ;  and  the  efforts  which  it  makes  to 
recover  its  equilibrium  produce  all  the  phenomena 
of  electricity. 

You  see,  then,  that  a  body  may  become  electric 
in  two  different  ways,  according  as  the  ether  con- 
tained in  its  pores  becomes  more  or  less  elastic  than 
that  which  is  external ;  hence  result  two  species  of 
electricity :  the  one,  by  which  the  ether  is  rendered 
more  elastic,  or  more  compressed,  is  denominated 
increased  or  positive  electricity ;  me  other,  in  which 
the  ether  is  less  elastic,  or  more  rarefied,  is  denom- 
inated diminished  or  negative  electricity.  The  phe- 
nomena of  both  are  nearly  the  same;  a  slight  differ- 
once  only  is  observable,  which  I  shall  mention. 

Bodies  are  not  naturally  electrical — as  the  elas- 
ticity of  the  ether  has  a  tendency  to  maintain  it  in 
equilibrio,  it  must  always  require  a  violent  operation 
to  disturb  this  equilibrium,  and  to  render  bodies 


NEGATIVE    ELECTRICITY.  93 

electrical ;  and  such  operations  must  act  on  bodies 
with  close  pores,  that  the  equilibrium,  once  deranged, 
may  not  be  instantly  restored.  We  accordingly  find 
that  glass,  amber,  sealing-wax,  or  sulphur  are  the 
bodies  employed  to  excite  electricity. 

The  easiest  operation  and  for  some  time  past, 
the  most  universally  known,  is  to  rub  a  stick  of  seal- 
ing-wax with  a  piece  of  woollen  cloth,  in  order  to 
communicate  to  that  wax  the  power  of  attracting 
small  slips  of  paper  and  of  other  light  bodies.  Am- 
ber, by  means  of  friction,  produces  the  same  phe- 
nomena; and  as  the  ancients  gave  to  this  body  the 
name  of  electrum,  the  power  excited  by  friction  ob- 
tained, and  preserves,  the  name  of  electricity — natural 
philosophers  of  the  remotest  ages  having  remarked 
that  this  substance  acquired  by  friction  the  faculty 
of  attracting  light  bodies. 

This  effect  undoubtedly  arises  from  the  derange- 
ment of  the  equilibrium  of  the  ether  by  means  of 
friction.  I  must  begin,  therefore,  with  explaining 
this  well-known  experiment.  Amber  and  sealing- 
wax  have  their  pores  abundantly  close,  and  those  of 
wool  are  abundantly  open ;  during  the  friction,  the 
pores  of  both  the  one  and  the  other  compress  them- 
selves, and  the  ether  which  is  contained  in  them  is 
reduced  to  a  higher  degree  of  elasticity.  According 
as  the  pores  of  the  wool  are  susceptible  of  a  com- 
pression greater  or  less  than  those  of  amber  or  seal- 
ing-wax, it  must  happen  that  a  portion  of  ether  shall 
pass  from  the  wool  into  the  amber,  or,  reciprocally, 
from  the  amber  into  the  wool.  In  the  former  case, 
the  amber  becomes  positively  electric,  and  in  the 
other  negatively — and  its  pores  being  close,  it  will 
remain  in  this  state  for  some  time;  whereas  the 
wool,  though  it  has  undergone  a  similar  change,  will 
presently  recover  its  natural  state. 

From  the  experiments  which  electric  sealing-wax 
furnishes,  we  conclude  that  its  electricity  is  negative, 
and  that  a  part  of  its  ether  has  passed  during  the 


94  OF    POSITIVE    AXD 

friction  into  the  wool.  Hence  you  perceive  how  a 
stick  of  sealing-wax  is,  by  friction  on  woollen  cloth, 
deprived  of  part  of  the  ether  which  it  contained, 
and  must  thereby  become  electric.  Let  us  now  see 
what  effects  must  result,  from  this,  and  how  far  they 
correspond  with  observation  and  experience. 

Let  A  B,  Fig.  39,  be  a  stick  of  sealing-- 
wax, from  which,  by  friction,  part  of  the     Fig.  39. 
ether  contained  in  its  pores  has  been  c 
forced  out ;  that  which  remains,  being     \ 
less  compressed,  will  therefore  have  less        \ 
force  to  expand  itself,  or,  in  other  words, 
will  have  less  elasticity  than  that  con- 
tained in  other  bodies  in  the  circumam- 
bient air :  but  as  the  pores  of  air  are  still 
closer  than  those  of  sealing-wax,  this 
prevents  the  ether  contained  in  the  air 
from  passing  into  the  sealing-wax,  to 
restore  the  equilibrium:  at  least  this 
will  not  take  place  till  after  a  consider- 
able interval  of  time. 

Let  a  small  and  very  light  body  C, 
whose  pores  are  open,  be  now  presented 
to  the  stick  of  sealing-wax,  the  ether 
contained  in  them,  finding  a  free  pass- 
age, because  it  has  more  force  to  expand 
itself  than  is  opposed  to  it  by  the  ether 
shut  up  in  the  stick  at  c,  will  suddenly  escape,  will 
force  a  passage  for  itself  through  the  air,  provided 
the  distance  is  not  too  great,  and  will  enter  into  the 
sealing-wax.  This  passage,  however,  will  not  be 
effected  without  very  considerable  difficulty,  as  the 
pores  of  the  sealing-wax  have  only  a  very  small 
aperture,  and  consequently  it  will  not  be  accom- 
panied with  a  vehemence  capable  of  putting  the  ether 
in  a  motion  of  agitation,  to  excite  a  sensible  light. 
A  faint  glimmering  only  will  be  perceptible  in  the 
dark,  if  the  electricity  is  sufficiently  strong. 


NEGATIVE    ELECTRICITY.  95 

But  another  phenomenon  will  be  observable  which 
is  no  less  surprising — the  small  body  C  will  spring 
towards  the  sealing-wax  as  if  attracted  by  it.  To 
explain  the  cause  of  this,  you  have  only  to  consider 
that  the  small  body  C,  in  its  natural  state,  is  equally 
pressed  on  all  sides  by  the  air  which  surrounds  it ; 
but  as  in  its  present  state  the  ether  makes  its  escape 
and  passes  through  the  air  in  the  direction  C  c,  it  is 
evident  that  this  last  fluid  will  not  press  so  violently 
on  the  small  body  on  this  side  as  on  any  other, 
and  that  the  pressure  communicated  to  it  towards  c 
will  be  more  powerful  than  in  any  other  direction, 
impelling  it  towards  the  sealing-wax  as  if  attracted 
by  it. 

Thus  are  explained,  in  a  manner  perfectly  intel- 
ligible, the  attractions  observable  in  the  phenomena 
of  electricity.  In  this  experiment,  the  electricity  is 
too  feeble  to  produce  more  surprising  effects.  I 
shall  have  the  honour  of  presenting  you  with  a  more 
ample  detail  in  the  following  Letters. 

Uh  July,  1761. 


LETTER  XXVIII. 

On  the  same  Subject. 

SUCH  were  the  faint  beginnings  of  the  electrical 
phenomena ;  it  was  not  till  lately  that  they  were 
carried  much,  farther.  At  first  a  tube  of  glass  was 
employed,  similar  to  that  of  which  barometers  are 
made,  but  of  a  larger  diameter,  which  was  rubbed 
with  the  naked  hand,  or  with  a  piece  of  woollen 
cloth,  and  electrical  phenomena  more  striking  were 
observed. 

You  will  readily  comprehend,  that  on  rubbing  a 
tube  of  glass,  part  of  the  ether  must  pass,  in  virtue 


96  OF   POSITIVE    AND 

of  the  compression  of  the  pores  of  the  glass,  and  of 
the  rubbing  body,  either  from  the  hand  into  the  glass, 
or  from  the  glass  into  the  hand,  according  as  the 
pores  of  the  one  or  of  the  other  are  more  susceptible 
of  compression  in  the  friction.  The  ether,  after 
this  operation,  easily  recovers  its  equilibrium  in  the 
hand,  because  its  pores  are  open ;  but  those  of  the 
glass  being  abundantly  close,  this  fluid  will  preserve 
its  state  in  it,  whether  the  glass  is  surcharged  or 
exhausted,  and  consequently  will  be  electric,  and 
will  produce  phenomena  similar  to  those  of  sealing- 
wax,  but  undoubtedly  much  stronger,  as  its  electri- 
city is  carried  to  a  higher  degree,  as  well  from  the 
greater  diameter  of  the  tube  as  from  the  very  nature 
of  glass. 

Experiments  give  us  reason  to  conclude  that  the 
tube  of  glass  becomes,  by  these  means,  surcharged 
with  ether,  whereas  sealing-wax  is  exhausted  of  it ; 
the  phenomena  however  are  nearly  the  same. 

It  must  be  observed  that  the  glass  tube  retains  its 
electricity  as  long  as  it  is  surrounded  only  with  air, 
because  the  pores  of  the  glass  and  those  of  the  air 
are  too  close  to  allow  a  communication  sufficiently 
free  to  the  ether,  and  to  exhaust  the  glass  of  what 
it  has  more  than  in  its  natural  state ;  superfluity  of 
ether  always  increasing  elasticity.  But  the  air  must 
be  very  dry,  for  only  when  in  that  state  are  its  pores 
sufficiently  close  ;  when  it  is  humid  or  loaded  with 
vapours,  experiments  do  not  succeed,  whatever  de- 
gree of  friction  you  bestow  on  the  glass.  The  reason 
is  obvious ;  for  water,  which  renders  the  air  humid, 
having  its  pores  very  open,  receives  every  instant 
the  superfluous  ether  which  was  in  the  glass,  and 
which  of  course  remains  in  its  natural  state.  Ex- 
periments succeed,  then,  in  only  very  dry  air :  let  us 
now  see  what  phenomena  a  glass  tube  will  in  that 
case  produce,  after  having  undergone  considerable 
friction. 


J3 


NEGATIVE    ELECTRICITY.  97 

It  is  clear  that  on  presenting  to  it  a  small  Fig.  40. 
light  body  C.  Fig.  40,  with  open  pores, 
such  as  gold  leaf,  the  ether  in  the  tube, 
more  elastic  at  the  nearest  parts,  D,  E, 
will  not  make  ineffectual  efforts  to  dis- 
charge itself  and  pass  into  the  pores  of 
the  body  C.  It  will  force  a  path  through 
the  air,  provided  the  distance  be  not  too 
great ;  and  you  will  even  see  a  light 
between  the  tube  and  the  body,  occa- 
sioned by  the  agitation  excited  in  the 
ether,  which  passes  with  difficulty  from 
the  tube  into  the  body.  When,  instead 
of  the  body  C,  the  finger  is  applied  to 
it,  you  feel  a  pricking,  occasioned  by 
the  rapid  entrance  of  the  ether ;  and  if 
you  expose  your  face  to  it  at  some  dis- 
tance, you  feel  a  certain  agitation  in  the 
air,  excited  by  the  transition  of  the  ether.  These 
circumstances  are  likewise  accompanied  sometimes 
with  a  slight  crackling,  produced  undoubtedly  by  the 
agitation  of  the  air,  which  the  ether  traverses  with 
such  rapidity. 

I  must  entreat  you  to  keep  in  mind,  that  an  agita- 
tion in  the  air  always  produces  a  sound,  and  that 
the  motion  of  ether  produces  light ;  and  then  the 
explanation  of  these  phenomena  will  become  abun- 
dantly easy. 

Let  the  small  light  body  C  be  replaced  in  the 
vicinity  of  our  electric  tube  ;  as  long  as  the  ether  is 
escaping  from  the  tube,  to  enter  into  the  pores  of  the 
body  C,  the  air  will  be  in  part  expelled  from  it,  and 
consequently  will  not  press  so  strongly  on  the  body 
on  that  side  as  in  every  other  direction  ;  it  will 
happen,  then,  as  in  the  preceding  case,  that  the  body 
C  will  be  impelled  towards  the  tube,  and  being  light, 
will  come  close  up  to  it.  We  see,  then,  that  this 
apparent  attraction  equally  takes  place,  whether  the 
ether  in  the  tube  be  too  much  or  too  little  elastic, 

VOL.  II.— I 


98       ON  THE  ELECTRIC  ATMOSPHERE. 

or  whether  the  elasticity  of  the  tube  be  positive  or 
negative.  In  both  cases,  the  passage  of  the  ether 
stops  the  air,  and  by  its  pressure  hinders  it  from 
acting. 

But  while  the  small  body  C  is  approaching  the 
tube,  the  passage  of  the  ether  becomes  stronger,  and 
the  body  C  will  soon  be  as  much  surcharged  with 
ether  as  the  tube  itself.  Then  the  action  of  the 
ether,  which  arises  from  its  elasticity  only,  entirely 
ceases,  and  the  body  C  will  sustain  on  all  sides  an 
equal  pressure.  The  attraction  will  cease,  and  the 
body  C  will  remove  from  the  tube,  as  nothing  detains 
it,  and  its  own  gravity  puts  it  in  motion.  Now,  as 
soon  as  it  removes,  its  pores  being  open,  its  super- 
fluous ether  presently  escapes  in  the  air,  and  it 
returns  to  its  natural  state.  The  body  will  then  act 
as  at  the  beginning,  and  you  will  see  it  again  approach 
the  tube,  so  that  it  will  appear  alternately  attracted 
and  repelled  by  it ;  and  this  play  will  go  on  till  the 
tube  has  lost  its  electricity.  For  as,  on  every 
attraction,  it  discharges  some  portion  of  its  super- 
fluous ether,  besides  the  insensible  escape  of  part  of 
it  in  the  air,  the  tube  will  soon  be  re-established  in 
its  natural  state,  and  in  its  equilibrium ;  and  this  so 
much  the  more  speedily  as  the  tube  is  small,  and  the 
body  C  light ;  then  all  the  phenomena  of  electricity 
will  cease. 

1th  July,  1761. 


LETTER  XXIX. 

On  the  Electric  Atmosphere. 

I  HAD  almost  forgotten  to  bring  forward  a  most 
essential  circumstance,  which  accompanies  all  elec- 
tric bodies,  whether  positively  or  negatively  such,  and 
which  supplies  some  very  striking  elucidations  for 
explaining  the  phenomena  of  electricity. 


ON  THE  ELECTRIC  ATMOSPHERE.       99 

Though  it  be  indubitably  true  that  the  pores  of 
air  are  very  close,  and  scarcely  permit  any  commu- 
nication between  the  ether  that  they  contain  and 
what  is  in  the  vicinity,  it  undergoes,  however,  some 
change  when  near  to  an  electric  body. 

Let  us  first  consider  an  electric  body  negatively  so, 
as  a  stick  of  sealing-  p^  93 

wax  A  B,  Fig.  92,  ^Bgg^&jm 
which  has  been  de-  ^; %lj-J-  1§%%6%% 
prived  by  friction  of  I 
part  of  the  ether  con-  *||S 
tained  in  its  pores,  so 
that  what  it  now  contains  has  less  elasticity  than 
that  of  other  bodies,  and  consequently  than  that  of 
the  air  which  surrounds  the  wax.  It  must  necessarily 
happen,  that  the  ether  contained  in  the  particles  of 
the  air  which  immediately  touch  the  wax,  as  at  m, 
having  greater  elasticity,  should  discharge  itself,  in 
however  small  a  degree,  into  the  pores  of  the  wax, 
and  will  consequently  lose  somewhat  of  its  elasticity. 
In  like  manner,  the  particles  of  air  more  remote, 
suppose  at  n,  will  likewise  suffer  a  portion  of  their 
ether  to  escape  into  the  nearer  at  m,  and  so  on  to  a 
certain  distance  beyond  which  the  air  will  no  longer 
undergo  any  change.  In  this  manner,  the  air  round 
the  stick  of  wax  to  a  certain  distance  will  be 
deprived  of  part  of  its  ether,  and  become  itself 
electric. 

This  portion  of  the  air,  which  thus  partakes  of  the 
electricity  of  the  stick  of  wax,  is  denominated  the 
electric  atmosphere ;  and  you  will  see  from  the  proofs 
which  I  have  just  adduced,  that  every  electric  body 
must  be  surrounded  with  an  atmosphere.  For  if 
the  body  is  positively  electric,  so  as  to  contain  a 
superfluity  of  ether,  it  will  be  more  compressed  in 
such  a  body,  and  consequently  more  elastic,  as  is 
the  case  with  a  tube  of  glass  when  rubbed ;  this  ether, 
more  elastic,  then  discharges  itself,  in  a  small  degree, 
into  the  particles  of  air  which  immediately  touch  it, 


100      ON  THE  ELECTRIC  ATMOSPHERE. 

and  thence  into  particles  more  remote,  to  a  certain 
distance ;  this  will  form  another  electric  atmosphere 
round  the  tube,  in  which  the  ether  will  be  more 
compressed,  and  consequently  more  elastic  than 
elsewhere. 

It  is  evident  that  this  atmosphere  which  surrounds 
such  bodies  must  gradually  diminish  the  electricity 
of  them,  as  in  the  first  case  there  passes  almost  con- 
tinually a  small  portion  of  ether  from  the  surround- 
ing air  into  the  electric  body,  and  which,  in  the 
other  case,  issues  from  the  electric  body  and  passes 
into  the  air.  This  is  likewise  the  reason  why 
electric  bodies  at  length  lose  their  electricity ;  and 
this  so  much  the  sooner,  as  the  pores  of  the  air 
are  more  open.  In  a  humid  air,  whose  pores  are 
very  open,  all  electricity  is  almost  instantly  extin- 
guished ;  but  in  very  dry  air  it  continues  a  consid- 
erable time. 

This  electric  atmosphere  becomes  abundantly 
sensible  on  applying  your  face  to  an  electrified 
body ;  you  have  a  feeling  similar  to  the  application 
of  a  spider's  web,  occasioned  by  the  gentle  transition 
of  the  ether  from  the  face  into  the  electric  body,  or 
reciprocally,  from  this  last  into  the  face,  according 
as  it  is  negative  or  positive,  to  use  the  common 
expression. 

The  electric  atmosphere  serves  likewise  more 
clearly  to  explain  that  alternate  attraction  and 
repulsion  of  light  bodies  placed  near  to  electric 
bodies  which  I  mentioned  in  the  preceding  Letter ; 
in  which  you  must  have  remarked,  that  the  explana- 
tion of  repulsion  there  given  is  incomplete ;  but  the 
electric  atmosphere  will  supply  the  defect. 

Let  A  B,  Pig.  93,  rep- 

resent  an    electric    tube      1,,  ,,,,!^' 

of  glass  surcharged  with  !  i  iiii^oi 

ether,  and  let  C  be  a  small 
light  body,  with  pores  suf- 
ficiently open,  in  its  nat- 
ural state.  Let  the  atmo- 


ON   THE    ELECTRIC    ATMOSPHERE.  101 

sphere  extend  as  far  as  the  distance  D  E.  Now,  as 
the  vicinity  of  C  contains  already  an  ether  more 
elastic,  this  will  discharge  itself  into  the  pores  of 
the  body  C ;  there  will  immediately  issue  from  the 
tube  a  new  ether,  which  will  pass  from  D  into  C, 
and  it  is  the  atmosphere  chiefly  which  facilitates 
this  passage.  For  if  the  ether  contained  in  the  air 
had  no  communication  with  that  in  the  tube,  the 
corpuscle  C  would  not  feel  the  vicinity  of  the  tube  ; 
but  while  the  ether  is  passing  from  D  to  C,  the 
pressure  of  the  air  between  C  and  D  will  be  dimin- 
ished, and  the  corpuscle  C  will  no  longer  be  pressed 
equally  in  all  directions;  it  will  therefore  be  im- 
pelled towards  D,  as  if  attracted  by  it.  Now,  in 
proportion  as  it  approaches,  it  will  be  likewise  more 
and  more  surcharged  with  ether,  and  will  become 
electric  as  the  tube  itself,  and  consequently  the 
electricity  of  the  tube  will  no  longer  act  upon  it. 

But.  as  the  corpuscle,  being  now  arrived  atD,  con- 
tains too  much  ether,  and  more  than  the  air  at  E,  it 
will  have  a  tendency  to  escape,  in  order  to  make  its 
way  to  E.  The  atmosphere  in  which  the  compres- 
sion of  the  ether  continues  to  diminish  from  D  to  E 
will  facilitate  this  passage,  and  the  superfluous  ether 
will  in  effect  flow  from  the  corpuscle  towards  E.  By 
this  passage,  the  pressure  of  the  air  on  the  corpuscle 
will  be  smaller  on  that  side  than  everywhere  else, 
and  consequently  the  corpuscle  will  be  carried 
towards  D,  as  if  the  tube  repelled  it.  But  as  soon 
as  it  arrives  at  E,  it  discharges  the  superfluous  ether, 
and  recovers  its  natural  state ;  it  will  then  be  again 
attracted  towards  the  tube,  and  having  reached  it, 
will  be  again  repelled,  for  the  reason  which  I  have 
just  been  explaining. 

It  is  the  electric  atmosphere  then  chiefly  which 

produces  these  singular  phenomena,  when  we  see 

electrified  bodies  alternately  attract  and  repel  small 

light  bodies,  such  as  little  slips  of  paper,  or  particles 

12 


102  COMMUNICATION    OF    ELECTRICITY 

of  metal,  with  which  this  experiment  best  succeeds, 
as  the  substances  have  very  open  pores. 

You  will  see,  moreover,  that  what  I  have  just  now 
said  respecting  positive  electricity  must  equally  take 
place  in  negative.  The  transition  of  the  ether  is 
only  reversed,  by  which  the  natural  pressure  of  the 
air  must  always  be  diminished. 

llth  July,  1761. 


LETTER  XXX. 

Communication  of  Electricity   to  a  Bar  of  Iron,  ly 
means  of  a  Globe  of  Glass. 

AFTER  the  experiments  made  with  glass  tubes,  we 
have  proceeded  to  carry  electricity  to  a  higher  de- 
gree of  strength.  Instead  of  a  tube,  a  globe  or 
round  ball  of  glass  has  been  employed,  which  is 
made  to  turn  with  great  velocity  round  an  axis,  and 
on  applying  the  hand  to  it,  or  a  cushion  of  some 
matter  with  open  pores,  a  friction  is  produced  which 
renders  the  globe  completely  electric. 

Fig.  94  represents  this  globe,  Fig.  94. 
which  may  be  made  to  move  round 
an  axis  A  B,  by  a  mechanism  simi- 
lar to  that  employed  by  turners. 
C  is  the  cushion  strongly  applied 
to  the  globe,  on  which  it  rubs  as  it 
turns  round.  The  pores  of  the 
cushion  being,  in  this  friction,  com- 
pressed more  than  those  of  the  glass,  the  ether  con- 
tained in  it  is  expelled,  and  forced  to  insinuate  itself 
into  the  pores  of  the  glass,  where  they  continue  to 
accumulate,  because  the  open  pores  of  the  cushion 
are  continually  supplying  it  with  more  ether,  which 
it  is  extracting,  at  least  in  part,  from  surrounding 
bodies ;  and  thus  the  globe  may  be  surcharged  with 
ether  to  a  much  higher  degree  than  glass  tubes. 


TO    A    BAR    OF    IRON.  103 

The  effects  of  electricity  are  accordingly  rendered 
much  more  considerable,  but  of  the  same  nature 
with  those  which  I  have  described,  alternately  at- 
tracting and  repelling  light  bodies ;  and  the  sparks 
which  we  see  on  touching  the  electric  globe  are 
much  more  lively. 

But  naturalists  have  not  rested  satisfied  with  such 
experiments,  but  have  employed  the  electrical  globe 
in  the  discovery  of  phenomena  much  more  sur- 
prising. 

Having  constructed  the  machine  for  turning  the 
globe  round  its  axis  A  B,  a  bar  of  iron  F  G,  Fig.  95, 
Fig.  95. 


is  suspended  above,  or  on  one  side  of  the  globe,  and 
towards  the  globe  is  directed  a  chain  of  iron  or  other 
metal  E  D,  terminating  at  D,  in  metallic  filaments, 
which  touch  the  globe.  It  is  sufficient  that  this  chain 
be  attached  to  the  bar  of  iron  in  any  manner  what- 
ever, or  but  touch  it.  When  the  globe  is  turned 
round,  and  in  turning  made  to  rub  on  the  cushion  at 


104  COMMUNICATION    OF   ELECTRICITY 

C,  in  order  that  the  glass  may  become  surcharged 
with  ether,  which  will  consequently  be  more  elastic, 
it  will  easily  pass  from  thence  into  the  filaments  D, 
for,  being  of  metal,  their  pores  are  very  open ;  and 
from  thence,  again,  it  will  discharge  itself  by  the 
chain  D  E,  into  the  bar  of  iron  F  G.  Thus,  by  means 
of  the  globe,  the  ether  extracted  from  the  cushion 
C  will  successively  accumulate  in  the  bar  of  iron 
F  G,  which  likewise,  of  consequence,  becomes  elec- 
tric ;  and  its  electricity  increases  in  proportion  as 
you  continue  to  turn  the  globe. 

If  this  bar  had  a  further  communication  with  other 
bodies  whose  pores  too  are  open,  it  would  soon  dis- 
charge into  them  its  superfluous  ether,  and  thereby 
lose  its  electricity;  the  ether  extracted  from  the 
cushion  would  be  dispersed  over  all  the  bodies  which 
had  an  intercommunication,  and  its  greatest  com- . 
pression  would  not  be  more  perceptible.  To  pre- 
vent this,  which  would  prove  fatal  to  all  the  phe- 
nomena of  electricity,  the  bar  must  of  necessity  be 
supported  or  suspended  by  props  of  a  substance 
whose  pores  are  very  close ;  such  as  glass,  pitch, 
sulphur,  sealing-wax,  and  silk.  It  would  be  proper, 
then,  to  support  the  bar  on  props  of  glass  or  pitch, 
or  to  suspend  it  by  cords  of  silk.  The  bar  is  thus 
secured  against  the  transmission  of  its  accumulated 
ether,  as  it  is  surrounded  on  all  sides  only  by  bodies 
with  close  pores,  which  permit  hardly  any  admission 
to  the  ether  in  the  bar.  The  bar  is  then  said  to  be 
insulated,  that  is,  deprived  of  all  contact  which  could 
communicate,  and  thereby  diminish,  its  electricity. 
You  must  be  sensible,  however,  that  it  is  not  possible 
absolutely  to  prevent  all  waste ;  for  this  reason,  the 
electricity  of  such  a  bar  must  continually  diminish, 
if  it  were  not  kept  up  by  the  motion  of  the  globe. 

In  this  manner  electricity  may  be  communicated 
to  a  bar  of  iron,  which  never  could  be  done  by  the 
most  violent  and  persevering  friction,  because  of  the 
openness  of  its  pores.  And,  for  the  same  reason, 


TO    A    BAR   OF    IRON.  105 

such  a  bar  rendered  electric  by  communication  pro- 
duces phenomena  much  more  surprising1.  On  pre- 
senting to  it  a  finger,  or  any  other  part  of  the  body, 
you  see  a  very  brilliant  spark  dart  from  it,  which, 
entering  into  the  body,  excites  a  pungent  and  some- 
times painful  sensation.  I  recollect  having  once 
presented  to  it  my  head,  covered  with  my  peruke 
and  hat,  and  the  stroke  penetrated  it  so  acutely  that 
I  felt  the  pain  next  day.* 

These  sparks,  which  escape  from  every  part  of  the 
bar  on  presenting  to  it  a  body  with  open  pores,  set 
on  fire  at  once  spirit  of  wine,  and  kill  small  birds 
whose  heads  are  exposed  to  them.  On  plunging 
the  end  of  the  chain  D  E  into  a  basin  filled  with 
water,  and  supported  by  bodies  with  close  pores, 
such  as  glass,  pitch,  silk,  the  whole  water  becomes 
electric  ;  and  some  authors  assure  us  that  they  have 
seen  considerable  lakes  electrified  in  this  manner,  so 
that  on  applying  the  hand  you  might  have  seen 
even  very  pungent  sparks  emitted  from  the  water. 
But  it  appears  to  me  that  the  globe  must  be  turned 
a  very  long  time  indeed,  to  convey  such  a  portion  of 
ether  into  a  mass  of  water  so  enormous ;  it  would  be 
likewise  necessary  that  the  bed  of  the  lake,  and 
every  thing  in  contact  with  it,  should  have  their 
pores  close. f 

The  more  open,  then,  the  pores  of  a  body  are,  the 
more  disposed  it  is  to  receive  a  higher  degree  of 
electricity,  and  to  produce  prodigious  effects.  You 
must  admit  that  all  this  is  perfectly  conformable  to 
the  principles  which  I  at  first  established. 

Uth  July,  1761. 


*  In  the  early  period  of  the  science,  the  results  of  electric  action, 
were  so  new  and  surprising  (hat  the  imaginations  of  many  persons 
were  highly  wrought  upon  by  them.  Musehenbroeck  asserted,  it  is  said, 
that  he  would  not  take  a  second  shock  for  the  kingdom  of  France. — Am. 
Ed. 

t  Such  an  effect  as  the  author  alludes  to  is  not  in  the  least  degree  prob- 
able.—Am.  Ed. 


106  ELECTRIZATION    OF 

* 

LETTER  XXXI. 

Electrization  of  Men  and  Animals. 

As  electricity  may  be  communicated  from  glass  to 
a  bar  of  iron,  by  means  of  a  chain  which  forms  that 
communication,  it  may  likewise  be  conveyed  into  the 
hunaan  body;  for  the  bodies  of  animals  have  this 
property  in  common  with  metals  and  water,  that 
their  pores  are  very  open ;  but  the  man  who  is  to 
be  the  subject  of  the  experiment  must  not  be  in 
contact  with  other  bodies  whose  pores  are  likewise 
open. 

For  this  purpose,  the  man  is  placed  on  a  large  lump 
of  pitch,  or  seated  on  a  chair  supported  by  glass 
columns,  or  a  chair  suspended  by  cords  of  silk,  as 
all  these  substances  have  pores  sufficiently  close  to 
prevent  the  escape  of  the  ether  with  which  the  body 
of  the  man  becomes  surcharged  by  electricity. 

This  precaution  is  absolutely  necessary,  for  were 
the  man  placed  on  the  ground,  the  pores  of  which 
are  abundantly  open,  as  soon  as  the  ether  was  con- 
veyed into  his  body  to  a  higher  degree  of  compres- 
sion, it  would  immediately  discharge  itself  into  the 
earth ;  and  we  must  be  in  a  condition  to  surcharge  it 
entirely  with  ether  before  the  man  could  become 
electric.  Now  you  must  be  sensible  that  the  cushion 
by  which  the  globe  of  glass  is  rubbed  could  not  pos- 
sibly supply  such  a  prodigious  quantity  of  ether,  and 
that  were  you  to  extract  it  even  out  of  the  earth 
itself,  you  could  gain  no  ground,  for  you  would  just 
take  away  as  much  on  the  one  hand  as  you  gave  on 
the  other. 

Having  then  placed  the  man  whom  you  mean  to 
electrify  in  the  manner  which  I  have  indicated,  you 
have  only  to  make  him  touch  with  his  hand  the 
globe  of  glass  while  it  turns,  and  the  ether  aeeumU' 


MEN    AND    ANIMALS.  107 

lated  in  the  globe  will  easily  pass  into  the  open  pores 
of  the  hand,  and  diffuse  itself  over  the  whole  body, 
from  whence  it  cannot  so  easily  escape,  as  the  air 
and  all  the  bodies  with  which  he  is  surrounded  have 
their  pores  close.  Instead  of  touching  the  globe 
with  his  hand,  it  will  be  sufficient  for  him  to  touch 
the  chain,  or  even  the  bar,  which  I  described  in  the 
preceding  Letter;  but  in  this  case,  not  only  the  man 
himself  must  be  surcharged  with  ether,  but  likewise 
the  chain  with  the  bar  of  iron ;  and  as  this  requires 
a  greater  quantity  of  ether,  it  would  be  necessary  to 
labour  longer  in  turning  the  globe,  in  order  to  supply 
a  sufficient  quantity.* 

In  this  manner  the  man  becomes  entirely  electric, 
or,  in  other  words,  his  whole  body  will  be  sur- 
charged with  ether ;  and  this  fluid  will  consequently 
be  found  there  in  the  highest  degree  of  compression 
and  electricity,  and  will  have  a  violent  tendency  to 
escape. 

You  must  be  abundantly  sensible  that  a  state  so 
violent  cannot  be  indifferent  to  the  man.  The  body 
is  in  its  minutest  parts  wholly  penetrated  with  ether, 
and  the  smallest  fibres  as  well  as  the  nerves  are  so 
filled  with  it,  that  this  ether,  without  doubt,  pervades 
the  principal  springs  of  animal  and  vital  motion.  It 
is  accordingly  observed,  that  the  pulse  of  a  man 
electrified  beats  faster — he  is  thrown  into  a  sweat — 
and  the  motion  of  the  more  subtile  fluids  with  which 
the  body  is  filled  becomes  more  rapid.  A  certain 
change  is  likewise  felt  over  the  whole  body,  which  it 
is  impossible  to  describe  ;  and  there  is  every  reason 
to  believe,  that  this  state  has  a  powerful  influence  on 
the  health,  though  sufficient  experiments  have  not 
yet  been  made  to  ascertain  in  what  cases  this  influ- 
ence is  salutary,  or  otherwise.  It  may  sometimes  be 


*  This  last  mode,  however,  of  performing  the  experiment,  would  be 
inch  the  better  of  the  two.— .Am.  Ed. 


108        ELECTRIZATION    OF    MEN    AND    ANIMALS. 

highly  beneficial  to  have  the  blood  and  humours 
raised  to  a  more  lively  circulation  ;  certain  obstruc- 
tions, which  threaten  dangerous  consequences,  might 
thereby  be  prevented ;  but  on  other  occasions  an 
agitation  too  violent  might  prove  injurious  to  health. 
The  subject  certainly  well  deserves  the  attention  of 
medical  gentlemen.  We  have  heard  of  many  sur- 
prising cures  performed  by  electricity,  but  we  are  not 
yet  enabled  sufficiently  to. distinguish  the  occasions 
on  which  we  may  promise  ourselves  success. 

To  return  to  our  eleqtrified  man ;  it  is  very  re- 
markable, that  in  the  dark  we  see  him  surrounded 
with  a  light  similar  to  that  which  painters  throw 
round  the  heads  of  saints.  The  reason  is  abundantly 
obvious  ;  as  there  is  always  escaping  from  the  body 
of  that  man  some  part  of  the  ether  with  which  he  is 
surcharged,  this  fluid  meets  with  much  resistance 
from  the  close  pores  of  the  air ;  it  is  thereby  put  into 
a  certain  agitation,  which  is  the  origin  of  light,  as  I 
have  had  the  honour  to  demonstrate. 

Phenomena  of  a  very  surprising  nature  are  re- 
marked in  this  state  of  a  man  electrified.  On  touch- 
ing him,  you  not  only  see  very  brilliant  sparks  issue 
from  the  part  which  you  touch,  but  the  man  feels 
besides  a  very  pungent  pain.  Further,  if  the  person 
who  touches  him  be  in  his  natural  state,  or  not 
electrified,  both  sensibly  feel  this  pain,  which  might 
have  fatal  consequences,  especially  if  he  were  touched 
in  the  head,  or  any  other  part  of  the  body  of  acute 
sensibility.  You  will  readily  comprehend,  then,  how 
little  indifferent  it  is  to  us,  that  a  part  of  the  ether 
contained  in  our  body  escape  from  it,  or  that  new 
ether  is  introduced,  especially  as  this  is  done  with 
such  amazing  rapidity. 

Moreover,  the  light  with  which  we  see  the  man 
surrounded  in  the  dark  is  an  admirable  confirmation 
of  my  remarks  respecting  the  electric  atmosphere 
which  is  diffused  round  all  bodies ;  and  you  will  no 


THE    TWO    SPECIES    OF    ELECTRICITY.  109 

longer  find  any  difficulty  in  the  greater  number  of 
electrical  phenomena,  however  inexplicable  they  may 
at  first  appear. 
18th  July,  1761. 


LETTER  XXXII. 

Distinctive  Character  of  the  two  Species  of  Electricity. 

You  will  please  to  recollect,  that  not  only  glass 
becomes  electric  by  friction,  but  that  other  sub- 
stances, such  as  sealing-wax  and  sulphur,  have  the 
same  property,  in  as  much  as  their  pores  are  likewise 
close  ;  so  that  whether  you  introduce  into  them  an 
extraordinary  quantity  of  ether,  or  extract  a  part  of 
it,  they  continue  for  some  time  in  that  state ;  nor  is 
the  equilibrium  so  soon  restored. 

Accordingly,  instead  of  a  globe  of  glass,  globes  of 
sealing-wax  and  sulphur  are  employed,  which  are 
likewise  made  to  revolve  round  an  axis,  rubbing  at 
the  same  time  against  a  cushion,  in  the  same  manne? 
which  I  described  respecting  a  globe  of  glass.  Such 
globes  are  thus  rendered  equally  electric ;  and  on 
applying  to  them  a  bar  of  iron,  which  touches  them 
only  by  slender  filaments  or  fringes  of  metal,  inca- 
pable of  injuring  the  globe,  electricity  is  immediately 
communicated  to  that  bar,  from  which  you  may 
afterward  transmit  it  to  other  bodies  at  pleasure. 

Here,  however,  a  very  remarkable  difference  is 
observable.  A  globe  of  glass  rendered  electric  in 
this  manner  becomes  surcharged  with  ether ;  and 
the  bar  of  iron,  or  other  bodies  brought  into  commu- 
nication with  it,  acquire  an  electricity  of  the  same 
nature.  This  electricity  is  denominated  positive  or 
augmented  electricity.  But  when  a  globe  of  sealing- 
wax  or  sulphur  is  treated  in  the  same  manner,  an 
electricity  directly  opposite  is  the  result,  which  is 
denominated  negative  or  diminished  electricity,  as 

VOL.  II.— K 


110  CHARACTER    OF    THE    TWO 

*t  is  perceived  that  by  friction  these  globes  are  de- 
Drived  of  part  of  the  ether  contained  in  their  pores. 

You  will  be  surprised  to  see  that  the  same  friction 
is  capable  of  producing  effects  altogether  opposite ; 
but  this  depends  on  the  nature  of  the  bodies  which 
undergo  the  friction,  whether  by  communicating  or 
receiving  it,  and  of  the  rigidity  of  their  particles 
which  contain  the  pores.  In  order  to  explain  the 
possibility  of  this  difference,  it  is  evident,  at  first 
sight,  that  when  two  bodies  are  rubbed  violently 
against  each  other,  the  pores  of  the  one  must  in 
most  cases  undergo  a  greater  compression  than 
those  of  the  other,  and  that  then  the  ether  contained 
in  the  pores  is  extruded,  and  forced  to  insinuate 
itself  into  those  of  the  bodies  which  are  less  com- 
pressed. 

It  follows,  then,  that  in  this  friction  of  glass  against 
a  cushion,  the  pores  of  the  cushion  undergo  a  greater 
compression  than  those  of  the  glass,  and  consequently 
the  ether  of  the  cushion  must  pass  into  the  glass, 
and  produce  in  it  a  positive  or  increased  electricity, 
as  I  have  already  shown.  But  on  substituting  a 
globe  of  sealing-wax  or  of  sulphur  in  place  of  the 
glass,  these  substances  being  susceptible  of  a  greater 
degree  of  compression  in  their  pores  than  the  sub- 
stance of  the  cushion  with  which  the  friction  is  per- 
formed, a  part  of  the  ether  contained  in  these  globes 
will  be  forced  out,  and  constrained  to  pass  into  the 
cushion ;  the  globe  of  sealing-wax  or  sulphur  will 
thereby  be  deprived  of  part  of  its  ether,  and  of  course 
receive  a  negative  or  diminished  electricity. 

The  electricity  which  a  bar  of  iron,  or  of  any  other 
metal,  receives  from  communication  with  a  globe 
of  sealing-wax  or  sulphur,  is  of  the  same  nature  ;  as 
is  also  that  which  is  communicated  to  a  man  placed 
on  a  lump  of  pitch,  or  suspended  by  cords  of  silk. 
When  such  a  man,  or  any  other  body  with  open 
pores  electrified  in  the  same  manner,  is  touched, 
nearly  the  same  php-nomena  are  observable  as  in  the 


SPECIES    OF    ELECTRICITY.  Ill 

case  of  positive  electricity.  The  touch  is  here  like- 
wise accompanied  with  a  spark,  and  a  puncture  on 
both  sides.  The  reason  is  obvious ;  for  the  ether 
which  in  this  case  escapes  from  bodies  in  their 
natural  state,  to  enter  into  electrified  bodies,  being 
under  constraint,  must  be  under  an  agitation  which 
produces  light.  A  sensible  difference  is,  however, 
to  be  remarked  in  the  figure  of  the  spark,  according 
as  the  electricity  is  positive  or  negative.  See  that 
of  positive  electricity,  Fig.  96. 


If  the  bar  A  B  possesses  positive  electricity,  and  the 
finger  C  is  presented  to  it,  the  light  which  issues  out 
of  the  bar  appears  under  the  form  of  rays  diverging 
from  the  bar  towards  the  finger  m  n,  and  the  luminous 
point  is  seen  next  the  finger. 

But  if  the  bar  A  B,  Fig.  97,  is  negatively  electric, 
Fig.  97. 

c 


and  the  ringer  C  is  presented  to  it,  the  luminous  rays 
m  n  diverge  from  the  finger,  and  you  see  the  lumi- 
nous point  p  next  the  bar. 

This  is  the  principal  character  by  which  positive 
is  distinguished  from  negative  electricity.  From 
whencesoever  the  ether  escapes,  the  spark  is  emitted 
in  the  figure  of  rays  diverging  from  that  point ;  but 
when  the  ether  enters  into  a  body,  the  spark  is  a 
luminous  point  towards  the  recipient  body.* 

QlstJuly,  1761. 

•  Professor  Hildebrand  has  lately  found  that  the  size  and  luminous- 
ness  of  the  spark  depend  upon  the  nature  as  we'll  as  upon  the  form  of 
the  metal  from  which  the  sparks  are  taken.  The  pieces  of  metal  which 
he  used  were  of  a  conical  form.  They  had  all  the  same  shape  and  dimeU- 


112         THE    TWO    SPECIES    OF    ELECTRICITY. 


LETTER  XXXIII. 

How  the  same  Globe  of  Glass  may  furnish  at  once  the 
two  Species  of  Electricity. 

You  will  be  enabled  to  see  still  more  clearly  the 
difference  between  positive  and  negative  electricity, 
after  I  have  explained  how  it  is  possible  to  produce 
by  one  and  the  same  globe  of  glass  both  the  species ; 
and  this  will  serve  at  the  same  time  further  to  elu- 
cidate these  wonderful  phenomena  of  nature. 

Let  A  B,  Fig.  98,  be  the  globe  of  glass  turning 
Fig.  98, 


eions,  and  were  fixed  in  the  same  manner,  at  the  end  of  an  insulated  con- 
ductor. The  sparks  differed  very  much  in  extent,  as  shown  in  the  follow- 
ing list ;  those  at  the  top  of  the  list  giving  the  greatest  sparks,  and  those 
at  the  bottom  the  least. 

Regulus  of  Sulphuret  of  Steel. 

Antimony.  Copper. 

Gold.  Tin.  Tempered  Steel. 

Silver.  Zinc. 

Brass.  Iron.    L«ad. 

A  cone  with  an  angle  of  52°  gave  a  much  more  luminous  spark  than  one 
with  an  angle  of  36°.  The  parabolic  rounding  of  the  summit,  or  slight 
inequalities  of  surface,  were  found  to  be  particularly  favourable  to  tUe 
production  of  a  strong  light. — Ed. 


THE    TWO    SPECIES   OF    ELECTRICITY.  113 

round  its  axis  C,  and  rubbed  against  the  cushion  D, 
in  an  opposite  direction  to  which  the  globe  is  touched 
by  the  metallic  filaments  F  attached  to  the  bar  of 
iron  F  G,  which  is  suspended  by  cords  of  silk  H  and 
I,  that  it  may  nowhere  touch  bodies  with  open 
pores. 

This  being  laid  down,  you  know  that  by  friction 
against  the  cushion  D,  the  ether  passes  from  the 
cushion  into  the  glass,  from  which  it  becomes  more 
compressed,  and  consequently  more  elastic  :  it  will 
pass,  therefore,  from  thence,  by  the  metallic  fila- 
ments F,  into  the  bar  of  iron  F  G ;  for  though  the 
pores  of  glass  are  abundantly  close,  as  the  ether  in 
the  globe  is  continually  accumulating  by  the  friction, 
it  soon  becomes  so  overcharged  that  it  escapes  by 
the  metallic  filaments,  and  discharges  itself  into  the 
bar,  by  which  this  last  becomes  equally  electric. 

Hence  you  perceive  that  all  this  superfluity  of 
ether  is  supplied  by  the  cushion,  which  would  speed- 
ily be  exhausted  unless  it  had  a  free  communication 
with  the  frame  which  supports  the  machine,  and 
thereby  with  the  whole  earth,  which  is  every  instant 
supplying  the  cushion  with  new  ether ;  so  that  as 
long  as  the  friction  continues,  there  is  a  quantity 
sufficient  further  to  compress  that  which  is  in  the 
globe  and  in  the  bar.  But  if  the  whole  machinery 
is  made  to  rest  on  pillars  of  glass,  as  M  and  N,  or 
if  it  is  suspended  by  cords  of  silk,  that  the  cushion 
may  have  no  communication  with  bodies  whose 
pores  are  open,  which  might  supply  the  deficiency 
of  ether,  it  would  soon  be  exhausted,  and  the  elec- 
tricity could  not  be  conveyed  into  the  globe  and  the 
bar  beyond  a  certain  degree,  which  will  be  scarcely 
perceptible  unless  the  cushion  be  of  a  prodigious 
size.  To  supply  this  defect,  the  cushion  D  is  put 
in  communication  with  a  large  mass  of  metal  E,  the 
ether  of  which  is  sufficient  to  supply  the  globe  and 
the  bar,  and  to  carry  it  to  such  a  high  degree  of 
compression 

s^-    * 


114         THE    TWO    SPECIES    OF    ELECTRICITY. 

You  will  thus  procure  to  the  globe  and  to  the  bar 
a  positive  electricity,  as  has  been  already  explained. 
But  in  proportion  as  they  become  surcharged  with 
ether,  the  cushion  and  the  metallic  mass  E  will  lose 
the  same  quantity,  and  thereby  acquire  a  negative 
electricity :  so  that  we  have  here  at  once  the  two 
species  of  electricity ;  the  positive  in  the  bar,  and 
the  negative  in  the  metallic  mass.  Each  produces 
its  effect  conformably  to  its  nature.  On  presenting 
a  finger  to  the  bar,  a  spark  with  divergent  rays  wiS 
issue  from  the  bar,  and  the  luminous  point  will  be 
seen  towards  the  finger ;  but  if  you  present  the  finger 
to  the  metallic  mass,  the  spark  with  divergent  rays 
will  issue  from  the  finger,  and  you  will  see  the  lu- 
minous point  towards  the  mass. 

Let  us  suppose  two  men  placed  on  lumps  of  pitch, 
to  cut  off  all  communication  between  them  and 
bodies  with  open  pores  ;  let  the  one  touch  the  bar, 
and  the  other  the  metallic  mass,  while  the  machine 
is  put  in  motion :  it  is  evident  that  the  former  will 
become  positively  electric,  or  surcharged  with  ether ; 
whereas  the  other,  he  who  touches  the  metallic 
mass,  will  acquire  a  negative  electricity,  and  lose 
his  ether. 

Here,  then,  are  two  electric  men,  but  in  a  manner 
totally  different,  though  rendered  such  by  the  same 
machine.  Both  will  be  surrounded  by  an  elec- 
tric atmosphere,  which  in  the  dark  will  appear  like 
the  light  that  painters  throw  about  the  figures  of 
saints.  The  reason  is,  that  the  superfluous  ether 
of  the  one  insensibly  escapes  into  the  circumambient 
air ;  and  that,  with  respect  to  the  other,  the  ether 
contained  in  the  air  insensibly  insinuates  itself  into 
his  body.  This  transition,  though  insensible,  will 
be  accompanied  with  an  agitation  of  ether,  which 
produces  light. 

It  is  evident  that  these  two  species  of  electricity 
are  directly  opposite ;  but  in  order  to  have  a  thorough 
conviction  of  it,  let  these  two  join  hands,  or  only 


THE    LEYDEN    EXPERIMENT.  115 

touch  each  other,  and  you  will  see  very  vehement 
sparks  issue  from  their  bodies,  and  they  themselves 
will  feel  very  acute  pain. 

If  they  were  electrified  in  the  same  manner,  which 
would  be  the  case  if  both  touched  the  bar  or  the 
metallic  mass,  they  might  safely  touch  each  other ; 
no  spark  and  no  pain  would  ensue,  because  the 
ether  contained  in  both  would  be  in  the  same  state ; 
whereas,  in  the  case  laid  down,  their  state  is  directly 
opposite.  .  "\ 

25th 'July,  1761. 


LETTER  XXXIV. 

The  Ley  den  Experiment. 

I  NOW  proceed  to  describe  a  phenomenon  of  elec- 
tricity which  has  made  a  great  deal  of  noise,  and 
which  is  known  by  the  name  of  the  Leyden  experi- 
ment, because  Mr.  Muschenbroeck,  professor  at  Ley- 
den,  is  the  inventor  of  it.*  What  is  most  astonish- 
ing in  this  experiment  is  the  terrible  stroke  resulting 
from  it,  by  which  several  persons  at  once  may  re- 
ceive a  very  violent  shock. 

Let  C,  Fig.  99,  be  a  globe  of  glass,  turned  round 
by  means  of  the  handle  E,  and  rubbed  by  th°  cushion 
D  D,  which  is  pressed  upon  the  globe  by  the  spring  O. 
At  Q  are  the  metallic  filaments  which  transmit  the 
electricity  into  the  bar  of  iron  F  G,  by  the  metallic 
chain  P.  < 

Hitherto  there  is  nothing  different  from  the  pro- 
cess already  described.  But  in  order  to  execute  the 

*  The  first  person  who  witnessed  the  shock  was  Cuneus,  a  clergyman 
of  Leyden .  Holding  a  tumbler  of  water  in  one  hand,  he  allowed  a  stream 
of  electric  fluid  to  pass  into  the  waier  through  a  wire,  which  hung  from 
the  prime  conductor,  to  ascertain  its  effects  upon  the  taste  of  the  water: 
When  he  thought  the  water  sufficiently  electrified,  he  was  about  to  re- 
move the  wire  with  his  other  hand ;  and,  on  touching  it,  to  his  great  as- 
louishment,  received  the  shock.—  Am.  Ed. 


116  THE    LEYDEN    EXPERIMENT. 

Fig.  99. 


experiment  in  question,  to  the  bar  is  attached  an- 
other chain  of  metal  H,  one  extremity  of  which  I  is 
introduced  into  a  glass  bottle  K  K,  filled  with  water ; 
the  bottle  too  is  placed  in  a  basin  L  L,  likewise  filled 
with  water.  You  plunge  at  pleasure  into  the  water 
in  the  basin  another  chain  A,  one  end  of  which  drags 
on  the  floor. 

Having  put  the  machine  in  motion  for  some  time, 
that  the  bar  may  become  sufficiently  electric,  you 
know  that  if  the  finger  were  to  be  presented  to  the 
extremity  of  the  bar  at  a,  the  usual  stroke  of  elec- 
tricity would  be  felt  from  the  spark  issuing  out  of 
it.  But  were  the  same  person  at  the  same  time  to 
put  the  other  hand  into  the  water  in  the  basin  at  A, 
or  were  he  but  to  touch  with  any  part  of  his  body 
the  chain  pUnged  in  that  water,  he  would  receive  a 
stroke  incomparably  more  violent,  by  which  his 
whole  frame  would  undergo  a  severe  agitation. 

This  shock  may  be  communicated  to  many  per- 
sons at  once.  They  have  only  to  join  hands,  or  to 
touch  each  other,  were  it  but  by  the  clothes  ;  then 
the  first  puts  his  hand  into  the  water  in  the  basin,  or 


THE    LEYDEN    EXPERIMENT.  117 

touches  the  chain  only,  one  end  of  which  is  plunged 
into  it ;  and  as  soon  as  the  last  person  applies  his 
finger  to  the  bar  5^ou  will  see  a  spark  dart  from  it 
much  more  vehement  than  usual,  and  the  whole 
chain  of  persons  feel,  at  the  same  instant,  a  very 
violent  shock  over  their  whole  body. 

Such  is  the  famous  Leyden  experiment,  which  is 
so  much  the  more  surprising,  that  it  is  difficult  to 
see  how  the  bottle  and  the  water  in  the  basin  con- 
tribute to  increase  so  considerably  the  effect  of  the 
electricity.  To  solve  this  .difficulty,  permit  me  to 
make  the  following  reflections. 

1.  While  by  the  action  of  the  machine  the  ether 
is  compressed  in  the  bar,  it  passes  by  the  chain  H 
into  the  water  contained  in  the  bottle  I,  and  there 
meeting  a  body  with  open  pores,  the  water  in  the 
bottle  will  become  as  much  surcharged  with  ether 
as  the  bar  itself. 

2.  The  bottle,  being  glass,  has  its  pores  close, 
and  therefore  does  not  permit  the  ether  compressed 
within  it  to  pierce  through  the  substance  of  the 
glass,  to  discharge  itself  into  the  water  in  the  basin ; 
consequently,  the  water  in  the  basin  remains  in  its 
natural  state,  and  will  not  become  electric  ;  or  even 
on  the  supposition  that  a  little  of  the  ether  might 
force  its  way  through  the  glass,  it  would  presently 
be  lost  in  the  basin  and  pedestal,  the  pores  of  which 
are  open. 

3.  Let  us  now  consider  the  case  of  a  man  with 
one  hand  in  the  water  in  the  basin,  or  only  in  con- 
tact with  the  chain  A,  one  extremity  of  which  is 
immersed  in  that  water ;  let  him  present  the  other 
hand  to  the  bar  at  a,  the  result  will  be  as  the  first 
effect,  that  with  the  spark  which  issues  from  the 
bar  the  ether  will  make  its  escape  with  great  ve- 
locity, and  meeting  everywhere  in  the  body  of  the 
man  open  pores,  will  without  obstruction  be  diffused 
over  it. 

4.  Hitherto  we  see  only  the  usual  effect  of  elec- 


118  THE    LEYDEN   EXPERIMENT. 

tricity ;  but  while  the  ether  with  such  rapidity  flies 
over  the  body  of  the  man,  it  discharges  itself  with 
equal  rapidity,  by  the  other  hand,  or  by  the  chain  A, 
into  the  water  in  the  basin ;  and  as  it  enters  this 
with  such  impetuosity,  it  will  easily  overcome  the 
obstacle  opposed  by  the  glass,  and  penetrate  into  the 
water  which  the  bottle  contains. 

5.  Now  the  water  in  the  bottle  containing  already 
an  ether  too  much  compressed,  it  will  acquire  from 
this  increase  new  force,  and  will  diffuse  itself  with 
impetuosity,   as  well  through  the  chain  I   H   as 
through  the  bar  itself :  it  will  of  consequence  make 
its  escape  thence  at  a  with  new  efforts  ;  and  as  this 
is  performed  in  an  instant,  it  will  enter  into  the  finger 
with  increased  force  to  be  diffused  over  the  whole 
body  of  the  man. 

6.  Passing  thence  anew  into  the  water  in  the  basin, 
and  penetrating  the  bottle,  it  will  increase  still  fur- 
ther the  agitation  of  the  ether  compressed  in  the 
water  of  the  bottle  and  in  the  bar ;  and  this  will  con- 
tinue till  the  whole  is  restored  to  equilibrium,  which 
will  quickly  take  place,  from  the  great  rapidity  with 
which  the  ether  acts. 

7.  The  same  thing  will  happen  if  you  employ 
several  persons  instead  of  one  man.     And  now  I 
flatter  myself,  you  fully  comprehend  whence  arises 
the  surprising  increase  of  force  in  the  electricity 
which  is  produced  by  this  experiment  of  Mr.  Mus- 
chenbroeck,  and  which  exhibits  effects  so  prodigious. 

8.  If  any  doubt  could  remain  respecting  what  I 
have  advaaced,  that  the  ether  compressed  in  the 
water  of  the  bottle  could  not  penetrate  through  the 
glass,  and  that  afterward  I  have  allowed  it  a  passage 
abundantly  free — such  doubt  will  vanish  when  it  is 
considered,  that  in  the  first  case  every  thing  is  in  a 
state  of  tranquillity,  and  in  the  last  the  ether  is  in  a 
terrible  agitation,  which  must  undoubtedly  assist  its 
progress  through  the  closest  passages. 

28th  July,  1761. 


NATURE    OF   ELECTRICITY.  119 


LETTER   XXXV. 

Reflections  on  the  Cause  and  Nature  of  Electricity,  and 
on  other  Means  proper  to  produce  it. 

AFTER  these  elucidations,  you  can  be  at  no  loss 
respecting  the  cause  of  the  prodigious  effects  ob- 
servable in  the  phenomena  of  electricity. 

Most  authors  who  have  treated  the  subject,  per- 
plex the  experiments  in  such  a  manner  that  they  are 
rendered  absolutely  unintelligible,  especially  when 
they  attempt  an  explanation.  They  have  recourse 
to  a  certain  subtile  matter,  which  they  denominate 
the  electric  fluid,  and  to  which  they  ascribe  qualities 
so  extravagant,  that  the  mind  rejects  them  with  con- 
tempt ;  and  they  are  constrained  to  acknowledge,  at 
length,  that  all  their  efforts  are  insufficient  to  furnish 
us  with  a  solid  knowledge  of  these  important  phe- 
nomena of  nature. 

But  you  are  enabled  to  conclude,  from  the  prin- 
ciples which  I  have  unfolded,  that  bodies  evidently 
become  electric  only  so  far  as  the  elasticity,  or  the 
state  of  the  compression  of  the  ether  in  the  pores  of 
bodies,  is  not  the  same  as  everywhere  else  ;  in  other 
words,  when  it  is  more  or  less  compressed  in  some 
than  in  others.  For  in  that  case  the  prodigious 
elasticity  with  which  the  ether  is  endowed  makes 
violent  efforts  to  recover  its  equilibrium,  and  to  re- 
store everywhere  the  same  degree  of  elasticity,  as 
far  as  the  nature  of  the  pores,  which  in  different 
bodies  are  more  or  less  open,  will  permit ;  and  it  is 
the  return  to  equilibrium  which  always  produces  the 
phenomena  of  electricity. 

When  the  ether  escapes  from  a  body  where  it  is 
more  compressed,  to  discharge  itself  into  another 
where  it  is  less  so,  this  passage  is  always  obstructed 
by  the  close  pores  of  the  air ;  hence  it  is  put  into  a 


120  ON    THE    CAUSE    AND 

certain  agitation,  or  violent  motion  of  vibration,  in 
which,  as  we  have  seen,  light  consists  ;  and  the  more 
violent  this  motion  is,  the  more  brilliant  the  light 
becomes,  till  it  is  at  length  capable  of  setting  bodies 
on  fire,  and  of  burning  them. 

While  the  ether  penetrates  the  air  with  so  much 
force,  the  particles  of  air  are  likewise  put  into  a  mo- 
tion of  vibration,  which  occasions  sound ;  it  is  ac- 
cordingly observed,  that  the  phenomena  of  electri- 
city are  accompanied  with  a  cracking  noise,  greater 
or  less,  according  to  the  diversity  of  circumstances. 

And  as  the  bodies  of  men  and  animals  are  filled 
with  ether  in  their  minutest  pores,  and  as  the  action 
of  the  nerves  seems  to  depend  on  the  ether  con- 
tained in  them,  it  is  impossible  that  men  and  animals 
should  be  indifferent  with  respect  to  electricity :  and 
when  the  ethe'r  in  them  is  put  into  a  great  agitation, 
the  effect  must  be  very  sensible,  and,  according  to 
circumstances,  sometimes  salutary,  and  sometimes 
hurtful.  To  this  last  class,  undoubtedly,  must  be 
referred  the  terrible  shock  of  the  Leyden  experi- 
ment ;  and  there  is  every  reason  to  believe  that  it 
might  be  carried  to  a  degree  of  force  capable  of  kill- 
ing men,  for  by  means  of  it  many  small  animals,  such 
as  mice  and  birds,  have  actually  been  killed. 

Though  friction  usually  is  employed  in  the  pro- 
duction of  electricity,  you  will  easily  comprehend 
that  there  may  be  other  means  besides  this.  What- 
ever is  capable  of  carrying  the  ether  contained  in  the 
pores  of  a  body  to  a  greater  or  less  degree  of  com- 
pression than  ordinary,  renders  it  electric :  and  if  its 
pores  are  close,  there  the  electricity  will  be  of  some 
duration ;  whereas,  in  bodies  whose  pores  are  open 
it  cannot  possibly  subsist,  unless  surrounded  by  air, 
or  other  bodies  with  close  pores. 

Hence  it  has  been  observed,  that  heat  frequently 
supplies  the  place  of  friction.  When  you  heat  or 
melt  sealing-wax  or  sulphur  in  a  spoon,  you  discover 
a  very  sensible  electricity  in  these  substances  after 


NATURE    OF   ELECTRICITY.  121 

they  are  cooled.  The  reason  is  no  longer  a  mystery, 
as  we  know  that  heat  enlarges  the  pores  of  all  bodies, 
for  they  occupy  a  greater  space  when  hot  than  when 
they  are  cold. 

You  know  that  in  a  thermometer  the  mercury 
rises  in  heat  and  falls  in  cold ;  because  it  occupies 
a  greater  space  when  it  is  hot,  and  fills  the  tube 
more  than  when  it  is  cold.  We  find,  for  the  same 
reason,  that  a  bar  of  iron  very  hot  is  always  some- 
what longer  than  when  cold — a  property  common  to 
all  bodies  with  which  we  are  acquainted. 

When,  therefore,  we  melt  by  fire  a  mass  of  seal- 
ing-wax or  sulphur,  their  pores  are  enlarged,  and 
probably  more  open ;  a  greater  quantity  of  ether  must 
of  course  be  introduced  to  fill  them.  When,  after- 
ward, these  substances  are  suffered  to  cool,  the  pores 
contract  and  close,  so  that  the  ether  in  them  is  re- 
duced to  a  smaller  space,  and  consequently  carried 
to  a  higher  degree  of  compression,  which  increases 
its  elasticity :  these  masses  will  acquire,  therefore, 
a  positive  electricity,  and  must  consequently  exhibit 
the  effects  of  it. 

This  property  of  becoming  electric  by  heat  is 
remarked  in  most  precious  stones.  Nay,  there  is 
a  stone  named  tourmaline,  which,  when  rubbed  or 
heated,  acquires  at  once  the  two  species  of  electri- 
city. The  ether  in  one  part  of  the  stone  is  expelled 
to  compress  more  that  which  is  in  the  other  part ; 
and  its  pores  are  too  close  to  permit  the  re-establish- 
ment of  the  equilibrium.* 
1st  August,  1761. 

*  Very  important  discoveries  have  been  made  since  the  time  of  Euler, 
respecting  the  production  of  electricity  hy  friction,  pressure,  and  heat. 
A  very  brief  notice  of  these  will  be  interesting  to  the  reader. 

Electricity  by  Friction.— Rock  crystal,  and  almost  all  the  precious 
stones,  acquire  positive  or  vitreous  electricity  with  whatever  substances 
they  are  rubbed  ;  and  on  the  other  hand,  resin,  sulphur,  bitumen,  &c. 
acquire  negative  or  resinous  electricity  when  rubbed  with  any  non-con- 
ducting substance.  Glass,  however,  when  polished,  gives  vitreous  elec- 
tricity by  friction,  whereas  it  gives  resinous  electricity  when  it  is  rough. 
Among  the  metals  zinc  and  bismuth  always  acquire  vitreous  electri- 

VOL.  II.— L 


122  NATURE    OF    THUNDER. 


LETTER  XXXVI. 

Nature  of  Thunder :  Explanations  of  the  Ancient  Phi- 
losophers, and  of  Descartes:  Resemblance  of  the 
Phenomena  of  Thunder  to  those  of  Electricity. 

I  HAVE  hitherto  considered  electricity  only  as  an 
object  of  curiosity  and  speculation  to  naturalists ;  but 

city  when  rubbed  with  a  piece  of  woollen  cloth,  while  tin  and  antimony 
always  acquire  resinous  electricity.  In  many  of  the  other  metals,  and 
in  various  other  substances,"the  results  are  often  irregular  and  anoma- 
lous, sometimes  one  kind  of  electricity  being  developed,  and  sometimes 
another.  The  most  striking  example  of  this  is  in  the  mineral  called 
kyanite,  some  crystals  of  which  always  acquire  resinous  electricity  by 
friction,  while  other  crystals  always  acquire  vitreous  electricity.  In  some 
of  these  crystals,  indeed,  vitreous  electricity  is  obtained  by  rubbing  one 
face,  and  resinous  electricity  by  rubbing  the  other.  For  further  informa- 
tion on  this  subject,  see  Haiiy's  Traitfd?  Mineralogie,  Paris,  J822,  vol.  i. 
p.  186;  and  the  Edinburgh  Encyclopaedia,  Article  ELECTRICITY,  vol. 
viii.  p.  430. 

Electricity  by  Pressure. — The  Abb£  Haiiy  discovered  the  method  of 
producing  electricity  by  pressure.  He  found  that  if  a  rhomb  of  Iceland 
spar  is  held  in  one  hand  by  two  of  its  opposite  edges,  and  if  with  two 
fingers  of  the  other  hand  two  of  its  opposite  faces  are  merely  touched,  it 
gives  out  vitreous  electricity.  When  pressure  is  applied  in  place  of  con- 
tact, the  effect  is  greatly  increased.  Ilaiiy  found  the  same  property 
in  topaz,  euclase,  arragonite,  fluate  of  lime,  carbonate  of  lead,  and 
hyalin  quart/,  ail  of  which  give  vitreous  electricity,  both  by  friction  and 
pressure.  Sulphate  of  barytes  and  sulphate  of  limn  give  no  electricity 
by  pressure.  Elastic  bitumen,  which  is  negatively  electrified  by  friction, 
is  also  negatively  electrified  by  pressure. 

Electricity  by  Heat.— The  property  possessed  by  tourmaline  of  be- 
coming electrical  by  heat  seems  to  have  been  known  to  the  ancients, 
When  tourmaline,  oxide  of  zinc,  borate  of  magnesia,  Auvergne  meso- 
type,  Greenland  mesotype,  scolezite,  and  mesolite,  are  heated,  one  ex- 
tremity of  the  crystal  developes  resinous  and  the  other  vitreous  elec- 
tricity, the  intensity  of  electricity  diminishing  rapidly  from  the  extremi- 
ties to  the  middle  or  neutral  point  of  the  crystal.  In  the  boracite  there 
are  eight  electrical  poles,  one  at  each  solid  angle  of  the  cube. 

When  these  minerals  again  reach  the  ordinary  temperature,  the  elec- 
tricity disappears ;  but  M.  Haiiy  has  lately  found,  that  it  then  passes  by 
a  reduction  of  temperature  to  the  opposite  state.  With  oxide  of  zinc 
and  tourmaline  he  invariably  found,  that  the  opposite  electricity  could 
be  developed  by  cold,  so  that  the  pole  which  possessed  vitreous  electricity 
when  it  was  hot  developed  resinous  electricity  when  it  was  cold.  When 
the  opposite  electricity  is  beginning  to  show  itself,,  the  two  poles  have 


NATURE    OF    THUNDER.  123 

you  will  presently  see,  not  without  some  degree  of 
surprise,  that  thunder  and  lightning,  as  well  as  all 
the  terrible  phenomena  which  accompany  them, 
derive  their  origin  from  the  same  principle ;  and  that 
in  these  nature  executes  on  the  great  scale  what 
naturalists  do  in  miniature  by  their  experiments. 

Those  philosophers  who  thought  they  saw  some 
resemblance  between  the  phenomena  of  thunder  and 
those  of  electricity  were  at  first  considered  as  vision- 
aries ;  and  it  was  imagined  that  they  made  use  of 
this  pretence  merely  as  a  cover  to  their  ignorance 
respecting  the  cause  of  thunder :  but,  you  will  soon 
be  convinced  that  every  other  explanation  of  these 
grand  operations  of  nature  is  destitute  of  founda- 
tion. 

In  truth,  every  thing  advanced  on  the  subject  pre- 
vious to  the  knowledge  of  electricity  was  a  mass  of 
absurdity,  and  little  calculated  to  convey  instruction 
respecting  any  of  the  phenomena  of  thunder. 

Ancient  philosophers  attributed  the  cause  of  it  to 


sometimes  at  once  both  vitreous  and  resinous  electricity.  The  disap- 
pearance of  the  opposite  electricity  produced  by  cold  takes  place  gen- 
erally below  the  freezing  point — SeeHauy's  Traite  de  Mineralogie,  torn, 
i.  p.  200. 

In  examining  the  electricity  of  the  tourmaline,  I  have  found  that  it 
may  be  shown  in  a  very  satisfactory  manner,  by  means  of  a  thin  slice 
taken  from  any  part  of  the  prism,  and  having  its  surfaces  perpendicular 
to  the  axis  of  the  prism.  It  must  then  be  placed  upon  a  piece  of  well 
polished  glass,  and  the  glass  heated  to  a  considerable  degree.  At  the 
proper  temperature,  which  is  about  that  of  boiling  water,  the  slice 
•will  adhere  to  the  glass  so  firmly,  that  even  when  the  glass  is  above 
the  tourmaline,  the  latter  will  adhere  to  it  for  six  or  eight  hours.  By 
this  means  slices  of  a  very  considerable  breadth  and  thickness  develop 
as  much  electricity  as  is  capable  of  supporting  their  own  weight.  The 
slice  of  tourmaline  adheres  equally  to  all  bodies  whatever.  Mr. 
Sivright  has  fitted  up  a  tourmaline  so  as  to  bring  the  action  of  its  two 
poles  very  near  to  one  another.  It  resembles  the  letter  D,  with  an 
opening  in  its  curved  part.  The  straight  part  is  the  tourmaline,  and 
the  two  curved  parts  are  pieces  of  silver  wire  rising  out  of  two  silver 
caps ;  one  of  which  embraces  each  pole  of  the  tourmaline.  A  pith 
ball  suspended  at  the  opening  vibrates  between  the  extremities  of  the 
wires.  Sir  H.  Davy  (Elements  of  Chymical  Philosophy,  vol.  i.  p.  130) 
states,  that  when  the  slice  is  of  considerable  size,  flashes  of  light  may  be 
seen  along  its  surface. — See  Edinburgh  Philosophical  Journal,  vol.  i. 
p.  205.— Ed. 


124  NATURE    OF   THUNDER. 

sulphureous  and  bituminous  vapours,  which,  ascend- 
ing from  the  earth  into  the  air,  mixed  with  the 
clouds,  where  they  caught  fire  from  some  unknown 
cause. 

Descartes,  who  quickly  perceived  the  insufficiency 
of  this  explanation,  imagined  another  cause  in  the 
clouds  themselves,  and  thought  that  thunder  might 
be  produced  by  the  sudden  fall  of  more  elevated 
clouds  on  others  in  a  lower  region  of  the  air ;  that 
the  air  contained  in  the  intermediate  space  was  com- 
pressed by  this  fall  to  such  a  degree  as  was  capable 
of  exciting  a  noise  so  loud,  and  even  of  producing 
lightning  and  thunder,  though  it  was  impossible  for 
him  to  demonstrate  the  possibility  of  it. 

But  without  fixing  your  attention  on  false  expla- 
nations, which  lead  to  nothing,  I  hasten  to  inform 
you  that  it  has  been  discovered  by  incontestable 
proofs  that  the  phenomena  of  thunder  are  always 
accompanied  by  the  most  indubitable  marks  of  elec- 
tricity. 

Let  a  bar  of  metal,  say  of  iron,  be  placed  on  a 
pillar  of  glass,  or  any  other  substance  whose  pores 
are  close,  that  when  the  bar  acquires  electricity  it 
may  not  escape  or  communicate  itself  to  the  body 
which  supports  the  bar ;  as  soon  as  a  thunder-storm 
arises,  and  the  clouds  which  contain  the  thunder 
come  directly  over  the  bar,  you  perceive  in  it  a  very 
strong  electricity,  generally  far  surpassing  that  which 
art  produces ;  if  you  apply  the  hand  to  it,  or  any 
other  body  with  open  pores,  you  see  bursting  from, 
it,  not  only  a  spark,  but  a  very  bright  flash,  with  a 
noise  similar  to  thunder ;  the  man  who  applies  his 
hand  to  it  receives  a  shock  so  violent  that  he  is 
stunned.  This  surpasses  curiosity ;  and  there  is  good 
reason  why  we  should  be  on  our  guard  and  not  ap- 
proach the  bar  during  a  storm. 

A  professor  at  Petersburg,  named  Richmann,  has 
furnished  a  melancholy  example.  Having  perceived 


NATURE    OF    THUNDER.  125 

a  resemblance  so  striking  between  the  phenomena 
of  thunder  and  those  of  electricity,  this  unfortunate 
naturalist,  the  more  clearly  to  ascertain  it  by  experi- 
ment, raised  a  bar  of  iron  on  the  roof  of  his  house, 
cased  below  in  a  tube  of  glass,  and  supported  by  a 
mass  of  pitch.  To  the  bar  he  attached  a  wire,  which 
he  conducted  into  his  chamber,  that  as  soon  as  the 
bar  should  become  electric,  the  electricity  might 
have  a  free  communication  with  the  wire,  and  so 
enable  him  to  prove  the  effects  in  his  apartment. 
And  it  may  be  proper  to  inform  you,  that  this  wire 
was  conducted  in  such  a  manner  as  nowhere  to  be 
in  contact  but  with  bodies  whose  pores  are  close, 
such  as  glass,  pitch,  or  silk,  to  prevent  the  escape 
of  the  electricity. 

Having  made  this  arrangement,  he  expected  a 
thunder-storm,  which,  unhappily  for  him,  soon  came. 
The  thunder  was  heard  at  a  distance  :  Mr.  Richmann 
was  all  attention  to  his  wire,  to  see  if  he  could  per- 
ceive any  mark  of  electricity.  As  the  storm  ap- 
proached, he  judged  it  prudent  to  employ  some  pre- 
caution, and  not  keep  too  near  the  wire ;  but  hap- 
pening carelessly  to  advance  his  chest  a  little,  he 
received  a  terrible  stroke,  accompanied  with  a  loud 
clap,  which  stretched  him  lifeless  on  the  floor. 
•  About  the  same  time,  the  late  Dr.  Lieberkuhn  and 
Dr.  Ludolf  were  preparing  to  make  similar  experi- 
ments in  this  city,  and  with  that  view  had  fixed  bars 
of  iron  on  their  houses  ;  but  being  informed  of  the 
disaster  which  had  befallen  Mr.  Richmann,  they  had 
the  bars  of  iron  immediately  removed ;  and,  in  my 
opinion,  they  acted  wisely. 

From  this  you  will  readily  judge,  that  the  air  or 
atmosphere  must  become  very  electric  during  a 
thunder-storm,  or  that  the  ether  contained  in  it  must 
then  be  carried  to  a  very  high  degree  of  compres- 
sion. This  ether,  with  which  the  air  is  surcharged, 
Will  pass  into  the  bar,  because  of  its  open  pores ; 
L9 


126  THE    PHENOMENA   OF 

and  it  will  become  electric,  as  it  would  have  been 
in  the  common  method,  but  in  a  much  higher  de- 
gree. 

4th  August,  1761. 


LETTER  XXXVII. 

Explanation  of  the  Phenomena   of  Lightning  and 
Thunder. 

THE  experiments  now  mentioned  incontestably 
demonstrate,  therefore,  that  stormy  clouds  are  ex- 
tremely electrical,  and  that  consequently  their  pores 
are  either  surcharged  with  ether,  or  exhausted,  as 
both  states  are  equally  adapted  to  electricity.  But 
I  have  very  powerful  reasons  for  believing  that  this 
electricity  is  positive,  that  the  ether  in  them  is  com- 
pressed to  the  highest  degree,  and  consequently  so 
much  the  more  elastic  than  elsewhere. 

Such  storms  usually  succeed  very  sultry  weather. 
The  pores  of  the  air,  and  of  the  vapours  floating  in 
it,  are  then  extremely  enlarged,  and  filled  with  a 
prodigious  quantity  of  ether,  which  easily  takes  pos- 
session of  all  the  empty  spaces  of  other  substances. 
But  when  the  vapours  collect  in  the  superior  re- 
gions of  our  atmosphere,  to  form  clouds,  they  have 
to  encounter  excessive  cold.  Of  this  it  is  impossible 
to  doubt,  from  the  hail  which  is  frequently  formed 
in  these  regions :  this  is  a  sufficient  proof  of  a  conge- 
lation, as  well  as  the  snow  which  we  find  on  the  tops 
of  very  high  mountains,  such  as  the  Cordilleras, 
while  extreme  heat  prevails  below. 

Nothing  then  is  more  certain,  or  better  established 
by  proof,  than  the  excessive  cold  which  universally 
prevails  in  the  upper  regions  of  the  atmosphere, 
where  clouds  are  formed.  It  is  equally  certain,  that 
cold  contracts  the  pores  of  bodies,  by  reducing  them 
to  a  smaller  size :  now,  as  the  pores  of  the  vapours 


LIGHTNING   AND   THUNDER.  127 

have  been  extremely  enlarged  by  the  heat,  as  soon 
as  they  are  formed  aloft  into  clouds,  the  pores  con- 
tract, and  the  ether  which  filled  them,  not  being  able 
to  escape,  because  those  of  the  air  are  very  close,  it 
must  needs  remain  there :  it  will  be  of  course  com- 
pressed to  a  much  higher  degree  of  density,  and 
consequently  its  elasticity  will  be  so  much  the 
greater. 

The  real  state  of  stormy  clouds,  then,  is  this — the 
ether  contained  in  their  pores  is  much  more  elastic 
than  usual,  or,  in  other  words,  the  clouds  have  a 
positive  electricity.  A  s  they  are  only  an  assemblage 
of  humid  vapours,  their  pores  are  very  open ;  but 
being  surrounded  by  the  air,  whose  pores  are  close, 
this  ether  could  not  escape  but  very  imperceptibly. 
But  if  any  person,  or  any  body  whatever  with  open 
pores,  were  to  approach  it,  the  same  phenomena 
which  electricity  exhibits  would  present  themselves ; 
a  very  vehement  spark,  or  rather  a  real  flash,  would 
burst  forth.  Nay  more,  the  body  would  undergo  a 
very  violent  shock  by  the  discharge,  from  the  inl- 
petuosity  with  which  the  ether  in  the  cloud  would 
rush  into  its  pqres.  This  shock  might  be  indeed  so 
violent  as  to  destroy  the  structure  ;  and,  finally,  the 
terrible  agitation  of  the  ether  which  bursts  from  the 
cloud,  being  not  only  light,  but  a  real  fire,  it  might 
be  capable  of  kindling  and  consuming  combustible 
bodies. 

Here,  then,  you  will  distinguish  all  the  circum- 
stances which  accompany  thunder;  and  as  to  the 
noise  of  thunder,  the  cause  is  very  obvious,  for  it  is 
impossible  the  ether  should  be  in  such  a  state  of 
agitation  without  the  air  itself  receiving  from  it 
the  most  violent  concussions,  which  forcibly  impel 
the  particles,  and  excite  a  dreadful  noise.  Thunder, 
then,  bursts  forth  as  often  as  the  force  of  ether 
contained  in  the  clouds  is  capable  of  penetrating 
into  a  body  where  the  ether  is  in  its  natural  state, 
and  whose  pores  are  open :  it  is  not  even  neces- 


128  PHENOMENA    OF 

sary  that  such  body  should  immediately  touch  the 
cloud. 

What  I  have  said  respecting  the  atmosphere  of 
electrified  bodies  principally  takes  place  in  clouds ; 
and  frequently,  during  a  storm,  we  are  made  sensible 
of  this  electric  atmosphere  by  a  stifling  air,  which  is 
particularly  oppressive  to  certain  persons.  As  soon 
as  the  cloud  begins  to  dissolve  into  rain,  the  air, 
becoming  humid  by  it,  is  charged  with  an  electricity, 
by  which  the  commotion  maybe  conveyed  to  bodies 
at  a  very  great  distance. 

It  is  observed  that  thunder  usually  strikes  very 
elevated  bodies,  such  as  the  summits  of  church-spires, 
when  they  consist  of  substances  with  open  pores,  as 
all  metals  are ;  and  the  pointed  form  contributes  not 
a  little  to  it.  Thunder  frequently  falls  likewise  on 
water,  the  pores  of  which  are  very  open ;  but  bodies 
with  close  pores,  as  glass,  pitch,  sulphur,  and  silk, 
are  not  greatly  susceptible  of  the  thunder-stroke, 
unless  they  are  very  much  moistened.  It  has  been 
accordingly  observed,  that  when  thunder  passes 
through  a  window,  it  does  not  perforate  the  glass, 
but  always  the  lead  or  other  substances  which  unite 
the  panes,  It  is  almost  certain,  that  an  apartment 
of  glass  cemented  by  pitch,  or  any  other  substance 
with  close  pores,  would  be  an  effectual  security 
against  the  ravages  of  thunder. 

8th  August,  1761. 


LETTER  XXXVIII. 

Continuation. 

THUNDER,  then,  is  nothing  else  but  the  effect  of 
the  electricity  with  which  the  clouds  are  endowed ; 
and  as  an  electrified  body,  applied  to  another  in  its 
natural  state,  emits  a  spark  with  some  noise,  and 
discharges  into  it  the  superfluous  ether  with  pro- 


LIGHTNING   AND  THUNDER.  129 

digious  impetuosity,  the  same  thing  takes  place  in  a 
cloud  that  is  electric,  or  surcharged  with  ether,  but 
with  a  force  incomparably  greater,  because  of  the 
terrible  mass  that  is  electrified,  and  in  which,  ac- 
cording to  every  appearance,  the  ether  is  reduced  to 
a  much  higher  degree  of  compression  than  we  are 
capable  of  producing  in  it  by  our  machinery. 

When,  therefore,  such  a  cloud  approaches  bodies 
prepared  for  the  admission  of  its  ether,  this  dis- 
charge must  be  made  with  incredible  violence  :  in- 
stead of  a  simple  spark,  the  air  will  be  penetrated 
with  a  prodigious  flash,  which,  exciting  a  commotion 
in  the  ether  contained  in  the  whole  adjoining  region 
of  the  atmosphere,  produces  a  most  brilliant  light ; 
and  in  this  lightning  consists. 

The  air  is  at  the  same  time  put  into  a  very  vio- 
lent motion  of  vibration,  from  which  results  the 
noise  of  thunder.  This  noise  must,  no  doubt,  be 
excited  at  the  same  instant  with  the  lightning ;  but 
you  know  that  sound  always  requires  a  certain 
quantity  of  time,  in  order  to  its  transmission  to  any 
distance,  and  that  its  progress  is  only  at  the  rate  of 
about  eleven  hundred  feet  in  a  second;  whereas 
light  travels  with  a  velocity  inconceivably  greater. 
Hence  we  always  hear  the  thunder  later  than  we 
see  the  lightning ;  and  from  the  number  of  seconds 
intervening  between  the  flash  and  the  report,  we  are 
enabled  to  determine  the  distance  of  the  place 
where  it  is  generated,  allowing  eleven  hundred  feet 
to  a  second. 

The  body  itself,  into  which  the  electricity  of  the 
cloud  is  discharged,  receives  from  it  a  most  dreadful 
stroke  ;  sometimes  it  is  shivered  to  pieces — some- 
times set  on  fire  and  consumed,  if  combustible — 
sometimes  melted,  if  it  be  of  metal ;  and,  in  such 
cases,  we  say  it  is  thunder-struck,  the  effects  of 
which,  however  surprising  and  extraordinary  they 
may  appear,  are  in  perfect  consistency  with  the  well- 
known  phenomena  of  electricity. 


130      PHENOMENA  OF  LIGHTNING  AND  THUNDER. 

A  sword,  it  is  known,  has  sometimes  been  by 
thunder  melted  in  the  scabbard,  while  the  last  sus- 
tained no  injury :  this  is  to  be  accounted  for  from 
the  openness  of  the  pores  of  the  metal,  which  the 
ether  very  easily  penetrates,  and  exercises  over  it 
all  its  powers ;  whereas  the  substance  of  the  scab- 
bard is  more  closely  allied  to  the  nature  of  bodies 
with  close  pores,  which  do  not  permit  the  ether  so 
free  a  transmission. 

It  has  likewise  been  found,  that  of  several  persons 
on  whom  the  thunder  has  fallen,  some  only  have 
been  struck  by  it ;  and  that  those  who  were  in  the 
middle  suffered  no  injury.  The  cause  of  this  phe- 
nomenon likewise  is  manifest.  In  a  group  exposed 
to  a  thunder-storm,  they  are  in  the  greatest  danger 
who  stand  in  the  nearest  vicinity  to  the  air  that  is 
surcharged  with  ether ;  as  soon  as  the  ether  is  dis- 
charged upon  one,  all  the  adjoining  air  is  brought 
back  to  its  natural  state,  and  consequently  those 
who  were  nearest  to  the  unfortunate  victim  feel  no 
effect;  while  others,  at  a  greater  distance,  where 
the  air  is  still  sufficiently  surcharged  with  ether,  are 
struck  with  the  same  thunder-clap. 

In  a  word,  all  the  strange  circumstances  so  fre- 
quently related  of  the  effects  of  thunder  contain 
nothing  which  may  not  be  easily  reconciled  with 
the  nature  of  electricity. 

Some  philosophers  have  maintained,  that  thundei 
does  not  come  from  the  clouds,  but  from  the  earth, 
or  from  bodies.  However  extravagant  this  senti- 
ment may  appear,  it  is  not  so  absurd,  as  it  is  difficult 
to  distinguish  in  the  phenomena  of  electricity 
whether  the  spark  issues  from  the  body  which  is 
electrified,  or  from  that  which  is  not  so,  as  it  equally 
fills  the  space  between  the  two  bodies ;  and  if  the 
electricity  is  negative,  the  ether  and  the  spark  are 
in  reality  emitted  from  the  natural  or  non-electrified 
body.  But  we  are  sufficiently  assured,  that  in  thun- 


OF  AVERTING  THE  EFFECTS  OF  THUNDER.     131 

der  the  clouds  have  a  positive  electricity,  and  that 
the  lightning  is  emitted  from  the  clouds. 

You  will  be  justifiable,  however,  in  asking,  if  by 
every  stroke  of  thunder  some  terrestrial  body  is 
affected  1  We  see,  in  fact,  that  it  very  rarely  strikes 
buildings,  or  the  human  body  ;  but  we  know,  at  the 
same  time,  that  trees  are  frequently  affected  by  it, 
and  that  many  thunder-strokes  are  discharged  into 
the  earth  and  into  the  water.  I  believe,  however, 
it  might  be  maintained,  that  a  great  many  do  not 
descend  so  low,  and  that  the  electricity  of  the  clouds 
is  very  frequently  discharged  into  the  air  or  atmo- 
sphere. 

The  small  opening  of  the  pores  of  the  air  no 
longer  opposes  any  obstruction  to  it,  when  vapours 
)r  rain  have  rendered  it  sufficiently  humid  ;  for  then 
we  know  the  pores  are  open. 

It  may  very  possibly  happen  in  this  case,  that  the 
superfluous  ether  of  the  clouds  should  be  discharged 
simply  into  the  air  ;  and  when  this  takes  place,  the 
strokes  are  neither  so  violent,  nor  accompanied  with 
so  great  a  noise,  as  when  the  thunder  bursts  on  the 
earth,  when  a  much  greater  extent  of  atmosphere  is 
put  in  agitation. 

llth  August,  1761. 


LETTER  XXXIX. 

The  Possibility  of  preventing,   and  of  averting,   the 
Effects  of  Thunder. 

IT  has  been  asked,  Whether  it  might  not  be  pos- 
sible to  prevent  or  to  avert  the  fatal  effects  of  thun- 
der 1  You  are  well  aware  of  the  importance  of  the 
question,  and  under  what  obligation  1  should  lay  a 
multitude  of  worthy  people,  were  I  able  to  indicate 
an  infallible  method  of  finding  protection  against 
thunder. 


132      OF  PREVENTING  AND  AVERTING 

The  knowledge  of  the  nature  and  effects  of  elec- 
tricity permits  me  not  to  doubt  that  the  thing  is 
possible.  I  corresponded  some  time  ago  with  a 
Moravian  priest,  named  Procopius  Divisch,  who  as- 
sured me  that  he  had  averted,  during  a  whole  sum- 
mer, every  thunder-storm  which  threatened  his  own. 
habitation  and  the  neighbourhood,  by  means  of  a 
machine  constructed  on  the  principles  of  electricity. 
Several  persons  since  arrived  from  that  country 
have  assured  me  that  the  fact  is  undoubted,  and 
confirmed  by  irresistible  proof. 

But  there  are  many  respectable  characters  whor 
on  the  supposition  that  the  thing  is  practicable, 
would  have  their  scruples  respecting  the  lawfulness 
of  employing  such  a  preservative.  The  ancient 
pagans,  no  doubt,  would  have  considered  him  as* 
impious  who  should  have  presumed  to  interfere 
with  Jupiter  in  the  direction  of  his  thunder.  Chris- 
tians, who  are  assured  that  thunder  is  the  work  of 
God,  and  that  Divine  Providence  frequently  employs 
it  to  punish  the  wickedness  of  men,  might  with 
equal  reason  allege  that  it  were  impiety  to  attempt 
to  oppose  the  course  of  sovereign  justice. 

Without  involving  myself  in  this  delicate  discus- 
sion, I  remark  that  conflagrations,  deluges,  and 
many  other  general  calamities  are  likewise  the 
means  employed  by  Providence  to  punish  the  sins 
of  men  ;  but  no  one  surely  ever  will  pretend,  that  it 
is  unlawful  to  prevent  or  resist  the  progress  of  a 
fire  or  an  inundation.  Hence  I  infer,  that  it  is  pei- 
fectly  lawful  to  use  the  means  of  prevention  against 
the  effects  of  thunder,  if  they  are  attainable. 

The  melancholy  accident  which  befell  Mr.  Rick' 
mann  at  Petersburg  demonstrates  that  the  thunder- 
stroke which  this  gentleman  unhappily  attracted  to 
himself,  would  undoubtedly  Have  fallen  somewhere 
else,  and  that  this  place  thereby  escaped ;  it  can 
therefore  no  longer  remain  a  question  whether  it  be 
possible  to  conduct  thunder  to  one  place  in  prefer- 


THE    EFFECTS    OF   THUNDER.  133 

ence  to  another ;  and  this  seems  to  bring  us  near 
our  mark. 

It  would  no  doubt  be  a  matter  of  still  greater  im- 
portance to  have  it  in  our  power  to  divest  the  clouds 
of  their  electric  force,  without  being  under  the 
necessity  of  exposing  any  one  place  to  the  ravages 
of  thunder ;  we  should  in  that  case  altogether  pre- 
vent these  dreadful  effects,  which  terrify  so  great  a 
part  of  mankind. 

This  appears  by  no  means  impossible ;  and  the 
Moravian  priest  whom  I  mentioned  above  unques- 
tionably effected  it ;  for  I  have  been  assured  that  his 
machinery  sensibly  attracted  the  clouds,  and  con- 
strained them  to  descend  quietly  in  a  distillation, 
without  any  but  a  very  distant  thunder-clap. 

The  experiment  of  a  bar  of  iron,  in  a  very  ele- 
vated situation,  which  becomes  electric  on  the 
approach  of  a  thunder-storm,  may  lead  us  to  the 
construction  of  a  similar  machine,  as  it  is  certain 
that  in  proportion  as  the  bar  discharges  its  electricity 
the  clouds  must  lose  precisely  the  same  quantity ; 
but  it  must  be  contrived  in  such  a  manner,  that  the 
bars  may  immediately  discharge  the  ether  which 
they  have  attracted. 

It  would  be  necessary  for  this  purpose  to  procure 
for  them  a  free  communication  with  a  pool,  or  with 
the  bowels  of  the  earth,  which,  by  means  of  their 
open  pores,  may  easily  receive  a  much  greater 
quantity  of  ether,  and  disperse  it  over  the  whole 
immense  extent  of  the  earth,  so  that  the  compres- 
sion of  the  ether  may  not  become  sensible  in  any 
particular  spot.  This  communication  is  very  easy, 
by  means  of  chains  of  iron,  or  any  other  metal, 
which  will  with  great  rapidity  carry  off  the  ether 
with  which  the  bars  are  surcharged. 

I  would  advise  the  fixing  of  strong  bars  of  iron, 
in  very  elevated  situations,  and  several  of  them  to- 
gether, their  higher  extremity  to  terminate  in  a 
point,  as  this  figure  is  very  much  adapted  to  the 

VOL.  II.— M 


134     OF  AVERTING  THE  EFFECTS  OF  THUNDER. 

attraction  of  electricity.  I  would  afterward  attach 
long  chains  of  iron  to  these  bars,  which  I  would 
conduct  under  ground  into  a  pool,  lake,  or  river, 
there  to  discharge  the  electricity ;  and  I  have  no 
doubt,  that  after  making  repeated  essays,  the  means 
may  be  certainly  discovered  of  rendering  such  ma- 
chinery more  commodious,  and  more  certain  in  its 
effect.* 

It  is  abundantly  evident,  that  on  the  approach  of 
a  thunder-storm,  the  ether  with  which  the  clouds 
are  surcharged  would  be  transmitted  in  great  abun- 
dance into  these  bars,  which  would  thereby  become 
very  electric,  unless  the  chains  furnished  to  the  ether 
a  free  passage,  to  spend  itself  in  the  water  and  in  the 
bowels  of  the  earth. 

The  ether  of  the  clouds  would  continue,  therefore, 
to  enter  quietly  into  the  bars,  and  would  by  its  agita- 
tion produce  a  light  which  might  be  visible  on  the 
pointed  extremities. 

Such  light  is,  accordingly,  often  observed  during 
a  storm  on  the  summit  of  spires — an  infallible  proof 
that  the  ether  of  the  cloud  is  there  quietly  discharg- 
ing itself;  and  every  one  considers  this  as  a  very 
good  sign  of  the  harmless  absorption  of  many  thun- 
der-strokes. 

Lights  are  likewise  frequently  observed  at  sea  on 
the  tops  of  the  masts  of  ships,  known  to  sailors  by 
the  name  of  Castor  and  Pollux  ;f  and  when  such  signs 
are  visible,  they  consider  themselves  as  safe  from 
the  stroke  of  thunder. 

Most  philosophers  have  ranked  these  phenomena 
among  vulgar  superstitions  ;  but  we  are  now  fully 

*  As  buildings  are  often  struck  laterally,  the  main  thunder-rod,  espe- 
cially in  monumental  pillars  and  elevated  buildings,  should  have  various 
lateral  branches  diverging  from  it,  and  extending  to  the  air  through 
openings  in  the  building.  By  this  means  it  is  secured  much  more 
effectually  than  when  there  is  only  one  conductor,  which  can  do  no 
more  than  protect  the  summit  of  the  building. — Ed. 

f  Thislphenomenon  is  also  called  the  Fire^of  St.  Elmo.  A  very  inter- 
esting account  of  it  will  be  found  in  the  Edinburgh  Philosophical  Jour- 
nal, vol.  ix.  p.  35.-Ed. 


ON    THE    LONGITUDE.  135 

assured  that  such  sentiments  are  not  without  foun- 
dation; indeed,  they  are  infinitely  better  founded 
than  many  of  our  philosophical  reveries.* 
15th  August,  1761. 


LETTER  XL. 

On  the  celebrated  Problem  of  the  Longitude  :  General 
Description  of  the  Earth,  of  its  Axis,  its  two  Poles, 
and  the  Equator. 

You  will  by  this  time,  no  doubt,  imagine  that 
enough  has  been  said  of  electricity ;  and  indeed  I 
have  nothing  further  to  add  on  that  subject ;  and  am, 
of  course,  not  a  little  embarrassed  about  the  choice 
of  one  worthy  of  your  attention. 

In  order  to  determine  my  choice,  I  think  myself 
obliged  to  take  into  consideration  those  subjects 
which  most  materially  interest  human  knowledge, 
and  which  authors  of  celebrity  most  frequently  bring 


*  A  very  copious  account  of  the  recent  discoveries  in  electricity  will  be 
found  in  the  article  on  that  subject,  in  the  Edinburgh  Encyclopaedia, 
vol.  viil.  p.  411. — Ed.  [It  is  remarkable  that  neither  Euler  nor  his  Eu- 
ropean editor  have  anywhere  noticed  the  discoveries  of  Dr.  Franklin, 
admitted  as  they  are,  almost  universally,  to  lie  at  the  foundation  of  the 
moat  intelligible  principles  of  the  science,  and  to  have  enriched  it  with 
the  most  useful  facts.  The  omission  is  the  more  surprising,  since  the 
experiments  of  the  American  philosopher  which  demonstrated  the  iden- 
tity of  lightning  and  the  fluid  of  an  electrical  machine  were  made  in  1752, 
nine  years  prior  to  the  date  of  Euler's  Letter;  and  that  his  letters  <o 
Peter  Collinson,  of  London,  describing  his  experiments  and  discoveriea, 
were  published  in  almost  all  the  languages  of  Europe,  and  more  eagerly 
read  than  any  thing  that  had  appeared  on  that  new  and  interesting  sub- 
ject. To  Dr.  Franklin  the  world  is  certainly  indebted  for  the  application 
of  the  rod  to  the  preservation  of  buildings.  His  views  also  of  the  nature 
of  electrical  agency  were  cordially  received  by  the  scientific  world,  and 
still  constitute  the  basis  of  the  prevailing  theory, — while  that  of  Euler 
never  attained  much  vogue  among  the  learned,  and  is  now  no  longer 
heard  of.  So  prominent  a  station  does  Dr.  Franklin  hold  among  the  most 
successful  cultivators  of  this  science,  and  so  numerous  are  the  facts 
which  have  been  added  since  his  day,  we  can  only  refer  the  reader  to 
Dr.  Priestley's  History  of  Electricity,  and  to  some  good  modern  treatises 
on  the  subject.— Am.  Ed.] 


136  ON    THE    LONGITUDE. 

forward.  These  are  subjects  respecting  which,  it  is 
to  be  presumed,  persons  of  quality  have  considerable 
information. 

As  you  must  unquestionably  have  heard  frequent 
mention  made  of  the  celebrated  problem  of  the  lon- 
gitude, for  the  solution  of  which  the  British  nation 
has  proposed  a  most  magnificent  premium,  I  presume 
that  my  labour  will  not  be  wholly  thrown  away  if  I 
employ  it  in  laying  before  you  a  fair  state  of  that 
important  question.  It  has  such  an  intimate  con- 
nexion with  the  knowledge  of  our  terraqueous  globe, 
that  it  were  a  shame  to  be  ignorant  of  it.  It  will 
accordingly  furnish  me  with  an  opportunity  of  ex- 
plaining a  variety  of  interesting  articles,  which  I 
flatter  myself  you  would  wish  to  see  elucidated. 

I  begin,  then,  with  a  general  description  of  the 
earth,  which  may  be  considered  as  a  globe,  though 
it  has  been  discovered  by  recent  observation  that  its 
real  figure  is  a  spheroid  somewhat  flattened ;  but  the 
difference  is  so  small  that  it  may  for  the  present  be 
altogether  neglected. 

The  first  thing  to  be  remarked  on  the  globe  of  the 
earth  are  two  points  on  its  surface  denominated  the 
two  poles  of  the  earth.  Round  these  two  points  the 
globe  of  the  earth  every  day  revolves,  as  you  turn 
a  ball  fixed  between  the  two  points  of  a  turning  ma- 
chine. This  motion  is  called  the  daily  or  diurnal 
motion  of  the  earth,  each  revolution  of  which  is  per- 
formed in  about  twenty-four  hours ;  or,  to  speak 
according  to  appearances,  you  know  that  the  whole 
heavens,  which  we  consider  as  a  concave  ball,  within 
whose  circumference  the  earth  revolver,  appear  to 
turn  round  the  earth  in  the  same  space  of  twenty- 
four  hours.  This  motion  is  likewise  performed 
round  two  fixed  points  in  the  heavens,  denominated 
the  poles  of  heaven ;  now  if  we  conceive  a  straight 
line  drawn  from  one  of  these  poles  of  heaven  to  the 
other,  that  line  will  pass  through  the  centre  of  the 
earth. 


ON   THE    LONGITUDE.  137 

But  you  will  easily  comprehend  that  the  appear- 
ance must  be  the  same,  whether  the  earth  turns  round 
these  poles  while  the  heavens  remain  in  a  state  of 
rest;  or  whether  the  heavens  revolve  round  their 
poles,  the  earth  remaining  at  rest.  On  either  sup- 
position we  are  equally  led  to  the  knowledge  of  the 
poles  of  the  earth,  the  foundation  not  only  of  astron- 
omy, but  likewise  of  geography. 

Let  Fig.  100  represent  the  globe  Fig.  100. 
of  the  earth,  whose  poles  are  at 
the  points  A  and  B ;  one  of  these 
poles,  A,  is  named  the  south  or  ant- 
arctic pole,  the  other,  B,  is  denom- 
inated the  north  or  arctic  pole.  This 
last  is  nearer  to  the  region  of  the 
globe  which  we  inhabit. 

I  remark  that  these  two  poles 
are  directly  opposite  to  each  other ;  in  other  words, 
were  a  straight  line  A  B  to  be  drawn  directly  through 
the  earth,  it  would  pass  precisely  through  the  mid- 
dle C,  that  is  to  say,  through  the  centre  of  the  earth. 
This  straight  line  A  B  has  accordingly  its  appro- 
priate name,  and  is  called  the  axis  of  the  earth,  which 
being  produced  in  both  directions  to  the  heavens, 
will  terminate  in  the  two  points  which  are  called  the 
poles  of  heaven ;  and  to  which  we  give  the  same 
names  as  to  those  of  the  earth. 

These  two  poles  of  the  earth  are  by  no  means  a 
mere  fiction,  or  a  speculation  of  astronomers  and 
geographers;  but  are  really  most  essential  points 
marked  on  the  surface  of  our  globe ;  for  it  is  well 
known,  that  the  nearer  we  approach  these  two  points, 
the  colder*  and  more  rugged  the  face  of  nature  be- 


*  I  have  lately  had  occasion  to  show,  that  the  greatest  cold  is  not  at 
the  poles,  but  at  two  points  on  each  side  of  the  pole,  nearly  coincident 
with  the  magnetic  poles.  The  mean  temperature  of  Melville  Island, 
which  Captain  Parry  found  to  be  l^o  for  1819-1820,  is  undoubtedly  lower 
than  that  of  the  north  pole  of  our  globe.— See  Edinburgh.  Transactions, 
vol  ix.  p.  201.— Ed. 

M2 


138  ON   THE    LONGITUDE. 

comes,  to  such  a  degree  that  the  regions  adjacent  to 
the  poles  are  absolutely  uninhabitable,  from  the  ex- 
cessive cold  which  prevails  there  during  the  winter. 
No  one  instance,  accordingly,  has  been  produced  of 
any  traveller,  whether  by  land  or  water,  who  has 
reached  either  of  the  poles.  It  may  be  affirmed, 
therefore,  that  these  two  spots  of  the  earth  are  alto- 
gether inaccessible. 

Having  thus  determined  the  two  poles  of  the  earth 
A  and  B,  we  may  conceive  the  whole  globe  divided 
into  two  hemispheres,  D  B  E  and  DAE,  each  of 
which  terminates  in  one  of  the  poles  as  its  summit. 
For  this  purpose  we  are  to  suppose  the  globe  bisected 
through  its  centre  0,  so  that  the  section  shall  be 
perpendicular  to  the  axis  of  the  earth  ;  this  section 
will  mark  on  the  surface  a  circle  encompassing  the 
whole  globe,  everywhere  equally  distant  from  the 
two  poles.  This  surrounding  circle  is  denominated 
the  equator.  The  regions  adjacent  to  it  are  the 
hottest,  and  on  that  account,  as  the  ancients  believed, 
almost  uninhabitable  ;  but  they  are  now  found  to  be 
exceedingly  populous,  though  the  heat  be  there 
almost  insupportable. 

But  as  you  remove  from  the  equator  on  either  side 
towards  the  poles,  the  countries  becomes  more  and 
more  temperate,  till  at  last,  on  approaching  too  near 
the  poles,  the  cold  becomes  intolerable. 

As  the  equator  divides  the  earth  into  two  hemi- 
spheres, each  bears  the  name  of  the  pole  contained 
in  it ;  thus  the  half  D  B  E,  which  contains  the  north 
pole,  is  denominated  the  northern  hemisphere,  and  in 
it  is  situated  all  Europe,  almost  the  whole  of  Asia, 
part  of  Africa,  and  the  half  of  America.  The  other 
hemisphere,  D  A  E,  is  from  its  pole  denominated  the 
southern  hemisphere,  and  contains  the  greater  part 
of  Africa,  the  other  half  of  America,  and  several 
isles,  which  geographers  attribute  to  Asia,  as  you 
will  recollect  to  have  seen  in  maps  o'  the  world. 

18th  August,  1761. 


MAGNITUDE  OF  THE  EARTH.        139 


LETTER  XLI. 

Of  the  Magnitude  of  the  Earth ;  of  Meridians,  and  the 
shortest  Road  from  Place  to  Place. 

HAVING  distinctly  fixed  the  idea  of  the  poles  of 
the  earth  and  of  the  equator,  which  you  much  more 
easily  imagine  on  a  globe  than  I  can  represent  by  a 
figure,  every  other  necessary  idea  will  readily  follow 
from  these. 

I  must,  however,  subjoin  a  further  elucidation  of 
considerable  importance.  The  axis  of  the  earth, 
passing  from  one  pole  to  the  other  through  the  cen- 
tre of  the  earth,  is  a  diameter  of  the  globe,  and  con- 
sequently is  double  the  length  of  the  radius.  A 
radius  of  the  earth,  or  the  distance  from  every  point 
on  the  surface  to  the  centre,  is  computed  to  be  3956 
English  miles ;  the  axis  of  the  earth  will  therefore 
contain  7912  English  miles.  And  the  equator  being 
a  circle  whose  centre  is  likewise  that  of  the  earth, 
it  will  have  nearly  the  same  radius,  namely  3956 
miles ;  the  diameter  of  the  equator  will  accordingly 
be  7912  miles,  and  its  whole  circumference  23,736 
miles  nearly :  so  that  if  you  were  to  make  a  tour  of 
the  globe,  following  the  track  of  the  equator,  you 
must  perform  a  journey  of  almost  23,736  English 
miles.  This  will  give  you  some  idea  of  the  magni- 
tude of  the  earth. 

The  equator  being  a  circle,  it  is  supposed  to  be 
divided  into  360  equal  parts,  named  degrees;  a  degree 
of  the  equator  contains,  therefore,  65  English  miles,* 
as  9  times  360  make  nearly  24,196. f 

*  These  results  are  only  approximative.  As  the  earth  is  a  spheroid, 
flattened  at  the  poles  like  an  orange,  the  circumference  of  the  meridian  is 
about  24,855.84  English  miles,  and  the  circumference  of  the  equator 
24,896.16  English  miles.  A  geographical  mile  of  60  to  a  degree  will 
therefore  contain  6075.6  English  feet.— Ed. 

t  This  paragraph,  as  it  stands,  is  unintelligible.  A  degree  at  the 
equator  is  about  69.2x360=  24,912,  the  circumference  of  the  earth.  The 
numbers  in  the  preceding  paragraph  are  still  more  erroneous.— Am.  Ed 


140  MAGNITUDE    OF    THE    EARTH. 

Every  degree  is  again  subdivided  into  60  equal 
parts,  called  minutes,  so  that  every  minute  contains 
more  than  an  English  mile,  or  6076  English  feet ;  r. 
second,  being  the  sixtieth  part  of  a  minute,  will  con- 
lain  101  English  feet. 

It  being  impossible  to  represent  a        Fig.  101. 

flobe  on  paper  any  other  way  than 
y  a  circle,  you  must  supply  this 
defect  by  imagination.  Accord- 
ingly, A  B,  Fig.  101,  being  the  two 
poles  of  the  earth,  B  the  north,  and 
A  the  south,  D  M  N  E  will  repre- 
sent the  equator,  or  rather  that  half 
of  it  which  is  turned  towards  us, 
the  other  being  concealed  on  the  opposite  side. 

The  line  D  M  N  E  represents,  then,  a  semicircle, 
as  well  as  B  E  A  and  B  D  A ;  all  these  semicircles 
having  their  centres  at  that  of  the  globe  C.  It  is 
possible  to  imagine  an  infinite  number  of  other  semi- 
circles, all  of  them  drawn  through  the  two  poles  of 
the  earth  A  and  B,  and  passing  through  every  point 
of  the  equator,  as  B  M  A,  B  N  A ;  these  will  all  be 
similar  to  the  first,  B  D  A  and  B  E  A,  though  in  the 
figure  their  form  appears  very  different.  Imagina- 
tion must  correct  this,  and  the  fact  is  apparent  on  a 
real  globe. 

All  these  semicircles  drawn  from  one  pole  to  the 
other,  through  whatever  point  of  the  equator  they 
may  pass,  are  denominated  meridians ;  or  rather,  a 
meridian  is  nothing  else  but  a  semicircle,  which  on 
the  surface  of  the  earth  is  drawn  from  one  pole  to 
the  other ;  and  you  can  easily  comprehend  that  tak- 
ing any  place  whatever  on  the  surface  of  the  earth, 
say  the  point  L,  you  can  always  conceive  a  meridian 
B  L  M  A,  which  passing  through  the  two  poles 
takes  in  its  way  the  point  L.  This  meridian,  then, 
is  named  the  meridian  of  L.  Supposing,  for  ex- 
ample, L  to  be  BerJm.  the  semicircle  B  L  M  A  would 


MAGNITUDE    OF    THE    EARTH.  141 

be  the  meridian  of  Berlin ;  and  the  same  may  be 
said  respecting1  every  other  spot  of  the  earth. 

You  can  represent  to  yourself  a  globe,  on  the 
surface  of  which  are  described  all  the  countries  of 
the  earth,  the  continent,  as  well  as  the  sea,  with  its 
islands.  This  artificial  globe,  denominated  the  ter- 
restrial or  terraqueous  globe,  yoir  must  no  doubt  be 
acquainted  with.  As  to  all  meridians  which  can 
possibly  be  drawn  upon  it,  and  a  great  number  of 
which  actually  are  traced,  I  remark,  that  each  being 
a  semicircle  is  divided  by  the  equator  into  two  equal 
parts,  each  of  which  is  the  fourth  part  of  a  circle, 
that  is,  an  arch  of  90  degrees.  Accordingly,  B  D, 
B  M,  B  N,  B  E,  are  fourth  parts  of  a  circle,  as  well 
as  A  D,  A  M,  A  N,  A  E  ;  each  therefore  contains 
90  degrees :  and  it  may  be  further  added,  that  each 
is  perpendicular  to  the  equator,  or  forms  right  angles 
with  it. 

Again,  were  a  person  to  travel  from  the  point  of 
the  equator  M  to  the  pole  B,  the  shortest  road  would 
be  to  pursue  the  track  of  the  meridian  MLB,  which 
being  an  arch  of  90  degrees,  will  contain  6214  Eng- 
lish miles ;  the  distance  to  be  passed  in  going  from 
the  equator  to  either  of  the  poles. 

You  will  recollect  that  the  shortest  road  from 
place  to  place  is  the  straight  line  drawn  through  any 
two  places ;  here  the  straight  line  drawn  from  the 
point  M  in  the  equator  to  the  pole  B  would  fall 
within  the  earth — a  route  which  it  is  impossible  to 
pursue,  for  we  are  so  attached  to  the  surface  of  the 
earth  that  we  cannot  remove  from  it.  For  this  rea- 
son, the  question  becomes  exceedingly  different 
when  it  is  asked,  What  is  the  shortest  road  leading 
from  one  spot  on  the  surface  of  a  globe  to  another  ? 
This  shortest  road  is  no  longer  a  straight  line,  but 
the  segment  of  a  circle,  described  from  one  point  of 
the  surface  to  another,  and  whose  centre  is  precisely 
that  of  the  globe  itself.  This  is  accordingly  in  per- 
fect Jiarmony  with  the  case  in  question;  for  to 


142        MAGNITUDE  OF  THE  EARTH. 

travel  from  the  point  M  in  the  equator  to  the  pole 
B,  the  arch  of  the  meridian  M  L  B,  which  I  have 
represented  as  the  shortest  road,  is  in  reality  a  seg- 
ment of  the  circle  whose  centre  is  precisely  that  of 
the  earth. 

In  like  manner,  if  we  consi'der  the  spot  L  situated 
in  the  meridian  B  L  M  A,  the  shortest  road  to  go 
thence  to  the  pole  B  Avill  be  the  arch  L  B  ;  and  if  we 
know  the  number  of  degrees  which  this  arch  con- 
tains, allowing  69  English  miles  to  a  degree,  we 
shall  have  the  length  of  the  road.  But  if  you  were 
disposed  to  travel  from  the  same  spot  to  the  equator 
by  the  shortest  track,  it  would  be  necessary  to  pur- 
sue the  track  of  the  arch  of  the  meridian  L  M,  the 
number  of  degrees  contained  in  which,  reckoning 
69  English  miles  to  a  degree,  would  give  the 
distance. 

We  must  be  satisfied  with  expressing  these  dis- 
tances in  degrees,  it  being  so  easy  to  reduce  them 
to  English  miles,  or  the  miles  of  any  other  nation. 
Taking,  then,  the  city  of  Berlin  for  the  spot  L,  we 
find  that  the  arch  L  M,  which  leads  to  the  equator, 
contains  52  degrees  and  a  half;  consequently,  to 
travel  from  Berlin  to  the  equator,  the  shortest  road 
is  3623  English  miles.  But  if  any  one  were  to  go 
from  Berlin  to  the  north  pole,  he  must  follow  the 
direction  of  the  arch  B  L,  which,  containing  37  de- 
grees and  a  half,  would  be  2591  English  miles. 
These  two  distances  added  give  6214  English  miles 
for  the  extent  of  the  arch  B  L  M,  which  is  the  fourth 
part  of  a  circle,  or  90  degrees,  which  contain,  as  we 
have  seen,  24,855  English  miles. 

22d  August,  1761. 


OF    LATITUDE.  143 


LETTER  XLII. 

Of  Latitude,  and  its  Influence  on  the  Seasons,  and  the 
Length  of  the  Day. 

I  BEGIN  once  more  with  the  same        pi.  102. 
figure  (Fig.  102),  which   must  by 
this  time  be  abundantly  familiar  to 
you.    The  whole  circle  represents 
the  globe  of  the  earth ;  the  points  A 
and  B  its  two  poles ;  B  the  north  or 
arctic,  and  A  the  south  or  antarctic  ; 
so  that  the  straight  line  B  A  drawn 
within  the  earth  and  passing  through 
its  centre  C,  is  the  axis  of  it.     Again,  D  M  E  is  the 
equator,  which  divides  it  into  two  hemispheres,  D  B  E 
the  northern,  and  DAE  the  southern. 

Let  us  now  take  any  spot  whatever,  say  L,  and 
draw  its  meridian  B  L  M  A,  which,  being  a  semicir- 
cle, passes  through  the  point  L,  and  the  two  poles 
B  and  A.  This  then  is  the  meridian  of  the  place  L, 
divided  by  the  equator  at  M  into  two  equal  parts, 
making  two-fourths  of  a  circle,  each  of  which  con- 
tains 90  degrees.  I  remark  further,  that  the  arch 
L  M  of  this  meridian  gives  us  the  distance  of  the 
place  L  from  the  equator,  and  that  the  arch  L  B 
expresses  the  distance  of  the  same  place  L  from  the 
pole  B. 

This  being  laid  down,  it  is  of  importance  to  ob- 
serve that  the  arch  L  M,  or  the  distance  of  L  from 
the  equator,  is  denominated  the  latitude  of  the  place 
L ;  so  that  the  latitude  of  any  place  on  the  globe  is 
nothing  else  but  the  arch  of  the  meridian  of  that 
place,  which  is  intercepted  between  the  equator  and 
the  given  place ;  in  other  words,  the  latitude  of  a 
place  is  the  distance  of  that  place  from  the  equator; 
expressing  such  distance  by  degrees,  the  quantity  of 
which  we  perfectly  know  as  each  degree  contains 
69  English  miles. 


144  OF    LATITUDE. 

You  will  readily  comprehend  that  this  distance 
must  be  distinguished  according  as  the  given  place 
is  in  the  northern  or  southern  hemisphere.  In  the 
former  case,  that  is,  if  the  given  place  is  in  the 
northern  hemisphere,  we  say  it  has  north  latitude; 
but  if  it  is  in  the  southern  hemisphere,  we  say  it  is 
in  south  latitude. 

Taking  Berlin  as  an  instance,  we  say  it  is  in  52 
degrees  and  32  minutes  of  north  latitude ;  the  lati- 
tude of  Magdeburg  is,  in  like  manner,  northern,  52 
degrees  and  8  minutes.  But  the  latitude  of  Batavia 
in  the  East  Indies  is  6  degrees  12  minutes  south ; 
and  that  of  the  Cape  of  Good  Hope,  in  Africa,  is 
likewise  south  33  degrees  55  minutes. 

I  remark,  by-the-way,  that  for  the  sake  of  abbre- 
viation, instead  of  the  word  degree  we  affix  a  small 
cipher  (°)  to  the  numeral  characters,  and  instead 
of  the  word  minute  a  small  slanting  bar  ('),  and  in- 
stead of  second  two  of  these  (") ;  thus  the  .latitude 
of  the  observatory  at  Paris  is  48°  50'  14"  N.,  that  is, 
48  degrees,  50  minutes,  and  14  seconds  north.  In 
Peru  there  is  a  place  named  Vlo,  whose  latitude  has 
been  found  to  be  17°  36'  15"  S.,  that  is,  17  degrees, 
36  minutes,  and  15  seconds  south.  Hence  you  will 
understand,  that  if  a  place  were  mentioned  whose 
latitude  was  0°  0'  0",  such  a  place  would  be  precisely 
under  the  equator,  as  its  distance  from  the  equator 
is  0,  or  nothing ;  and  in  this  case  it  is  unnecessary 
to  affix  the  letter  N  or  S.  But  were  it  possible  to 
reach  a  place  whose  latitude  was  90°  N.,  it  would  be 
precisely  the  north  pole  of  the  earth,  which  is  dis- 
tant from  the  equator  the  fourth  of  a  circle,  or  90 
degrees.  This  will  give  you  a  clear  idea  of  what  is 
meant  by  the  latitude  of  a  place,  and  why  it  is  ex- 
pressed by  degrees,  minutes,  and  seconds. 

It  is  highly  important  to  know  the  latitude  of 
every  place,  not  only  as  essential  to  geography,  in 
the  view  of  assigning  to  each  its  exact  situation  on 
geographical  charts,  but  likewise  because  on  the 


OF    LATITUDE.  ]45 

latitude  depend  the  seasons  of  the  year,  the  inequali- 
ties of  day  and  night,  and  consequently  the  temper- 
ature of  the  place.  As  to  places  situated  directly 
under  the  equator,  there  is  scarcely  any  perceptible 
variation  of  the  seasons;  and  through  the  whole 
year  the  days  and  nights  are  of  the  same  length, 
namely,  12  hours.  For  this  reason  the  equator  is 
likewise  denominated  the  equinoctial  line;  but  in 
proportion  as  you  remove  from  the  equator,  the  more 
remarkable  is  the  difference  in  the  seasons  of  the 
year,  and  the  more  likewise  the  days  exceed  the 
nights  in  summer ;  whereas,  reciprocally,  the  days 
in  winter  are  as  much  shorter  than  the  nights. 

You  know  that  the  longest  days,  in  these  northern 
latitudes,  are  towards  the  commencement  of  our  sum- 
mer, about  the  21st  of  June ;  the  nights,  of  conse- 
quence, are  then  the  shortest :  and  that  towards  the 
beginning  of  our  winter,  about  the  23d  of  December, 
the  days  are  shortest  and  the  nights  longest :  so  that 
everywhere  the  longest  day  is  equal  to  the  longest 
night.  Now  in  every  place  the  duration  of  the 
longest  day  depends  on  the  latitude  of  the  place. 
Here,  at  Berlin,  the  longest  day  is  16  hours  and  38 
minutes,  and  consequently  the  shortest  day  in  winter 
is  7  hours  22  minutes.  In  places  nearer  the  equator, 
or  whose  latitude  is  less  than  that  of  (Berlin,  which  is 
52°  32',  the  longest  day  in  summer  is  less  than  16 
hours  38  minutes,  and  in  winter  the  shortest  day  is 
more  than  7  hours  22  minutes.  The  contrary  of 
this  takes  place  on  removing  farther  from  the  equa- 
tor: at  Petersburg,  for  example,  whose  latitude  is 
59°  56',  the  longest  day  is  18  hours  30  minutes, 
and  consequently  the  night  is  then  only  5  hours  30 
minutes :  in  winter,  on  the  contrary,  the  longest 
night  is  18  hours  30  minutes,  and  then  the  day  is 
only  5  hours  30  minutes.  Were  you  to  remove  still 
farther  from  the  equator,  till  you  came  to  a  place 
whose  latitude  was  66°  30',  the  longest  day  there 
would  be  exactly  24  hours,  in  other  words,  the  sun 

VOL.  II.— N 


146  OF    PARALLELS. 

would  not  set  at  that  place  at  that  season  ;  whereas 
in  winter  the  contrary  takes  place,  the  sun  not  rising 
at  all  on  the  23d  of  December,  that  is,  the  night 
then  lasting  24  hours.  Now  at  places  still  more 
remote  from  the  equator,  and  consequently  nearer 
the  pole,  for  example,  at  Warthuys,  in  Swedish  Lap- 
land, this  longest  day  lasts  for  the  space  of  several 
days  together,  during  which  the  sun  absolutely  never 
sets ;  and  the  longest  night,  when  the  sun  never  rises 
at  all,  is  of  the  same  duration. 

Were  it  possible  to  reach  the  pole  itself,  we  should 
have  day  for  six  months  together,  and  during  the 
other  six  perpetual  night.  From  this  you  compre- 
hend of  what  importance  it  is  to  know  accurately  the 
latitude  of  every  spot  of  the  globe. 

22d  August,  1761. 


LETTER  XLIII. 

Of  Parallels,  of  the  First  Meridian,  and  of  Longitude. 

HAVING  informed  you,  that  in  order  to  find  the 
meridian  of  any  given  place  L,  it  is  necessary  to 
draw  on  the  surface  of  the 
earth  a  semicircle  B  L  M  A, 
passing  through  the  two 
poles  B  and  A,  and  through 
the  given  place  L ;  I  remark, 
Fig.  103,  that  there  is  an 
infinite  number  of  other 
places  through  which  this 
same  meridian  passes,  and 
which  are  consequently  all 
said  to  be  situated  under 
the  same  meridian,  whether 
in  the  northern  hemisphere,  between  B  and  M,  or  in 
the  southern,  between  M  and  A. 

Now,  all  the  places  situated  under  the  same  me- 


OF    PARALLELS.  147 

ridian  differ  as  to  latitude,  some  being  nearer  to,  or 
more  remote  from,  the  equator  than  others.  Thus, 
the  meridian  of  Berlin  passes  through  the  city  of 
Meisse,  and  nearly  through  the  port  of  Trieste,  as 
well  as  many  other  places  of  less  note. 

You  will  likewise  please  to  observe,  that  a  great 
many  places  may  have  the  same  latitude,  that  is, 
may  be  equally  distant  from  the  equator,  but  all  of 
them  situated  under  different  meridians.  In  fact,  if 
L  is  the  city  of  Berlin,  whose  latitude,  or  the  arch  L  M, 
contains  52°  32',  it  is  possible  that  there  should  be 
under  any  other  meridian  B  N  A,  a  place  I,  the  lati- 
tude of  which,  or  the  arch  I  N,  shall  likewise  be 
52°  32' ;  such  are  the  points  F  and  G,  taken  in  the 
meridians  B  D  A,  B  E  A.  And  as  a  meridian  may  be 
drawn  through  every  point  of  the  equator,  in  which 
there  shall  be  a  place  whose  latitude  is  the  same  with 
that  of  Berlin,  or  the  place  L,  we  shall  have  an  in- 
finite number  of  places  all  of  the  same  latitude. 
They  will  be  all  situated  in  the  circle  F  L I  G,  all  the 
points  of  which  being  equally  distant  from  the  equa- 
tor, it  is  denominated  a  parallel  circle  to  the  equator, 
or  simply  a  parallel.  A  parallel  on  the  globe,  then, 
is  nothing  else  but  a  circle  parallel  to  the  equator, 
that  is,  all  the  points  of  which  are  equidistant  from 
it ;  hence  it  is  evident  that  all  the  points  of  a  parallel 
are  likewise  equidistant  from  the  poles  of  the  earth. 
As  it  is  possible  to  draw  such  a  parallel  through 
every  place  on  the  globe,  we  can  conceive  an  infinite 
number  of  them,  all  differing  in  respect  of  latitude, 
each  having  a  latitude,  whether  north  or  south,  pe- 
culiar to  itself. 

You  must  likewise  be  abundantly  sensible,  that  the 
greater  the  latitude  is,  or  the  nearer  you  approach  to 
either  of  the  poles,  the  smaller  the  parallels  become ; 
till  at  last,  on  coming  to  the  very  poles,  where  the 
latitude  is  90°,  the  parallel  is  reduced  to  a  single 
point.  But,  on  the  contrary,  as  you  approach  the 
equator,  or  the  smaller  the  latitude  is,  the  greater 


148  OF    PARALLELS. 

are  the  parallels;  till  at  last,  when  the  latitude 
becomes  0,  or  nothing,  the  parallel  is  lost  in  the 
equator.  It  is  accordingly  by  the  latitude  that  we 
distinguish  them ;  thus,  the  parallel  of  30°  is  that 
which  passes  through  every  place  whose  latitude  is 
30  degrees  ;  but  it  is  necessary  to  explain  yourself 
according  as  you  mean  north  or  south  latitude. 

On  consulting  an  accurate  map,  you  will  observe 
that  Hanover  is  situated  under  the  same  parallel 
with  Berlin,  the  latitude  of  both  being  52°  32' ;  and 
that  the  cities  of  Brunswick  and  Amsterdam  fall 
nearly  under  the  same  parallel;  but  that  the  me- 
ridians passing  through  these  places  are  different.  If 
you  know  the  meridian  and  the  parallel  under  which 
any  place  is  situated,  you  are  enabled  to  ascertain  its 
actual  position  on  the  globe.  If  it  were  affirmed,  for 
example,  that  a  certain  place  is  situated  under  the 
meridian  B  N  A,  and  the  parallel  F  L  G,  you  would 
only  have  to  look  where  the  meridian  B  N  A  is  inter- 
sected by  the  parallel  F  L  G,  and  the  point  of  inter- 
section I,  will  give  the  true  position  of  the  given 
place. 

Such  are  the  means  employed  by  geographers  to 
determine  the  real  situation  of  every  place  on  the 
face  of  the  globe.  You  have  only  to  ascertain  its 
parallel,  or  the  latitude,  and  its  corresponding  me- 
ridian. As  to  the  parallel,  it  is  easy  to  mark  and 
distinguish  it  from  every  other ;  you  have  only  to 
indicate  the  latitude  or  distance  from  the  equator, 
according  as  it  is  north  or  south :  but  how  describe 
a  meridian,  and  distinguish  it  from  every  other? 
They  have  a  perfect  resemblance,  they  are  all  equal 
to  each  other,  and  no  one  has  a  special  and  distinctive 
mark.  It  depends  therefore  upon  ourselves  to  make 
choice  of  a  certain  meridian,  and  to  fix  it,  in  order 
to  refer  all  others  to  that  one.  If,  for  example,  in 
Fig.  103,  (p.  146),  referred  to  at  the  beginning,  we 
were  to  fix  on  the  meridian  B  D  A,  it  would  be  easy 
to  indicate  every  other  meridian,  say  B  M  A,  by  simply 


OF    PARALLELS.  149 

ascertaining  on  the  equator  the  arch  D  M,  contained 
between  the  fixed  meridian  B  D  A  and  the  one  in 
question  B  M  A,  adding  only  in  what  direction  you 
proceed  from  the  fixed  meridian  towards  the  other, 
whether  from  east  to  west,  or  west  to  east. 

This  fixed  meridian,  to  which  every  other  is  re- 
ferred, is  called  the  first  meridian ;  and  the  choice 
of  this  meridian  being  arbitrary,  you  will  not  think 
it  strange  that  different  nations  should  have  made  a 
different  choice.  The  French  have  fixed  on  the  isle 
of  Ferro,  one  of  the  Canaries,  for  this  purpose,  and 
draw  their  first  meridian  through  it.  The  Germans 
and  Dutch  draw  theirs  through  another  of  the  Canary 
islands,  called  Teneriffe.  But  whether  you  follow 
the  French  or  German  geographers,  it  is  always 
necessary  carefully  to  mark  on  the  equator  the  point 
through  which  the  first  meridian  passes ;  from  this 
point  you  afterward  reckon  by  degrees  the  points 
through  which  all  other  meridians  pass ;  and  both 
French  and  Germans  have  agreed  to  reckon  from 
west  to  east.* 

If,  therefore,  in  Fig.  103,  (p.  146),  to  which  I  have 
already  referred,  the  semicircle  B  D  A  be  the  first 
meridian,  and  the  points  of  the  equator  M  and  N  were 
situated  towards  the  east,  you  have  only,  in  order  to 
mark  any  other  meridian,  say  B  M  A,  to  indicate  the 
magnitude  of  the  arch  D  M ;  and  this  arch  is  what 
we  call  the  longitude  of  all  the  places  situated  under 
the  meridian  B  M  A.  In  like  manner,  all  the  places 
situated  under  the  meridian  B  N  A  have  their  longitude 
determined  by  the  arch  of  the  equator  D  N,  expressed 
in  degrees,  minutes,  and  seconds. 

29th  August,  1761. 

*  In  English  maps  the  meridian  of  Greenwich,  a  village  near  London, 
where  the  Royal  Observatory  is  situated,  is  made  the  first  meridian.  In 
American  maps  the  meridian  of  the  city  of  Washington  is  generally 
taken.— Am.  Ed. 

N2 


150  FIRST    MERIDIAN. 

LETTER  XLIV. 

Choice  of  the  First  Meridian. 

You  have  now  received  complete  information 
respecting-  what  is  denominated  the  latitude  and  the 
longitude  of  a  place  on  the  surface  of  the  globe. 
Latitude  is  computed  on  the  meridian  of  the  given 
place,  up  to  the  equator ;  in  other  words,  it  is  the 
distance  of  the  parallel  passing  through  that  place 
from  the  equator  ;  and  to  prevent  all  ambiguity,  it  is 
necessary  to  express  whether  this  latitude  or  distance 
is  north  or  south. 

As  to  longitude,  we  must  determine  the  distance 
of  the  meridian  of  the  given  place  from  the  first  me- 
ridian ;/and  this  distance  is  computed  on  the  equator, 
from  the  first  meridian  to  the  meridian  of  the  given 
place,  always  proceeding  from  west  to  east ;  in  other 
words,  longitude  is  the  distance  of  the  meridian  of 
the  given  place  from  the  first  computing  the  degrees 
on  the  equator,  as  I  have  just  now  said. 

We  always  compute,  then,  from  the  first  meridian 
eastward ;  and  it  is  evident,  that  when  we  have  com- 
puted up  to  360  de'grees,  we  are  brought  back  pre- 
cisely to  the  first  meridian,  as  360  degrees  complete 
the  circumference  of  the  equator.  Accordingly, 
were  any  particular  place  found  to  be  in  the  359th 
degree  of  longitude,  the  meridian  of  that  place  would 
be  only  one  degree  distant  from  the  first  meridian, 
but  towards  the  west.  In  like  manner,  350°  of  lon- 
gitude would  exactly  correspond  with  a  distance  of 
10°  westward.  For  this  reason,  in  order  to  avoid 
all  ambiguity  in  determining  longitude,  we  go  on  to 
reckon  up  to  360°  towards  the  east. 

You  will  no  doubt  have  the  curiosity  to  know 
why  geographers,  in  settling  the  first  meridian,  have 
agreed  to  fix  on  one  of  the  Canary  Islands.  I  beg 


FIRST    MERIDIAN.  151 

leave  to  reply,  that  the  intention  was  to  begin  with 
settling  the  limits  of  Europe  towards  the  west ;  and 
as  these  islands,  called  the  Canaries,  and  situated  in 
the  Atlantic  Ocean,  beyond  Spain,  towards  America, 
were  still  considered  as  part  of  Europe,  it  was 
thought  proper  to  draw  the  first  meridian  through 
the  most  remote  of  the  Canary  Islands,  that  we 
might  be  enabled  to  compute  the  other  meridians 
without  interruption,  not  only  all  over  Europe,  but 
through  the  whole  extent  of  Asia ;  from  whence, 
going  on  to  reckon  towards  the  east,  we  arrive  at 
America,  and  thence  return  at  length  to  the  first 
meridian. 

But  to  which  of  the  Canary  Isles  shall  we  give 
the  preference  ?  Certain  geographers  of  France 
made  choice  of  the  isle  of  Ferro,  and  the  Germans 
that  of  Tenerifle,  because  the  real  situation  of  these 
isles  was  not  then  sufficiently  ascertained,  and  it  was 
not  perhaps  known  which  of  them  was  the  most 
remote ;  besides,  the  German  geographers  imagined 
that  the  mountain  named  the  Peak  of  Teneriffe  was 
pointed  out,  as  it  were,  by  the  hand  of  Nature  for 
the  first  meridian. 

Be  this  as  it  may,  it  seems  rather  ridiculous  to 
draw  the  first  meridian  through  a  place  whose  real 
position  on  the  globe  is  not  perfectly  determined ; 
for  it  was  not  till  very  lately  that  the  situation  of  the 
Canaries  was  ascertained.  For  this  reason  the  most 
accurate  astronomers  fix  the  first  meridian  precisely 
20  degrees  distant  from  that  of  the  observatory  at 
Paris,  without  regarding  through  what  spot  the  first 
may  in  that  case  pass ;  and  it  is  undoubtedly  the 
surest  method  that  can  be  adopted ;  and  in  order  to 
determine  every  other  meridian,  the  simplest  way  is 
to  find  out  its  distance  from  that  of  Paris :  then,  if 
that  other  meridian  is  more  to  the  east,  you  have 
only  to  add  to  it  20  degrees,  in  order  to  have  the 
longitude  of  the  places  situated  under  it ;  but  if  this 
meridian  be  westward  to  that  of  Paris,  you  must 


152  FIRST   MERIDIAN. 

subtract  the  distance  from  20  degrees.  Finally,  if 
this  distance  towards  the  west  is  more  than  20  de- 
grees, you  subtract  it  from  380  degrees,  that  is,  from 
20  degrees  above  360,  in  order  to  have  the  longitude 
of  the  meridian. 

Thus,  the  meridian  of  Berlin  being  to  the  eastward 
of  the  meridian  of  Paris  11°  2',  the  longitude  of 
Berlin  will  be  31°  2' ;  and  this  is  likewise  the  longi- 
tude of  all  other  places  situated  under  the  same 
meridian  with  Berlin. 

In  like  manner,  the  meridian  of  Petersburg  being 
28°  more  to  the  east  than  that  of  Paris,  the  longi- 
tude of  Petersburg  will  be  48°. 

The  meridian  of  St.  James's,  London,  is  more  to 
the  west  than  that  of  Paris  by  2°  25'  15" ;  subtract- 
ing, therefore,  that  quantity  from  20°,  the  remainder, 
17°  34'  45",  gives  the  longitude  of  St.  James's, 
London. 

Let  us  now  take  the  city  of  Lima  in  Peru,  the 
meridian  of  which  is  79°  27  46 "  to  the  westward  of 
that  of  Paris ;  that  distance  must  be  subtracted  from 
380  degrees;  which  will  leave  a  remainder  of  310° 
32'  15",  the  longitude  of  Lima.* 

Now,  when  the  latitude  and  longitude  of  a  place 
are  known,  we  are  enabled  to  ascertain  its  true  po- 
sition on  the  terrestrial  globe,  or  on  ,a  map  ;  for  as 
the  latitude  marks  the  parallel  under  which  the 
place  is  situated,  and  the  meridian  gives  the  me- 
ridian of  the  same  place,  the  point  where  the  parallel 
intersects  the  meridian  will  be  exactly  the  place  in 
question. 

You  have  but  to  look  at  a  map,  that  of  Europe, 
for  example,  and  you  will  see  the  degrees  of  the 
parallels  marked  on  both  sides,  or  their  distances 
from  the  equator ;  above  and  below  are  the  degrees 


*  This  method  of  reckoning  the  longitude  is  now  entirely  abandoned. 
The  English  reckon  it  from  Greenwich,  the  French  from  Paris,  and  so 
on.— Ed. 


OP    DETERMINING    THE    LATITUDE.  153 

of  longitude,  or  the  distances  of  the  several  me- 
ridians from  the  first. 

The  parallels  and  meridians  are  usually  traced  on 
maps,  degree  by  degree,  sometimes  at  the  distance 
of  five  degrees  from  each  other.  In  most  maps  the 
meridians  are  drawn  up  and  down,  and  the  parallels 
from  left  to  right :  the  upper  part  is  directed  towards 
the  north,  the  under  to  the  south,  the  right-hand 
side  towards  the  east,  and  the  left-hand  side  towards 
the  west. 

It  is  likewise  to  be  remarked,  that  as  all  the  me- 
ridians meet  at  the  two  poles,  the  more  any  two  me- 
ridians approach  to  either  of  the  poles  the  smaller 
their  distance  becomes ;  at  the  equator  their  distance 
always  is  greatest.  Accordingly  on  all  good  maps, 
where  the  meridians  are  traced,  you  will  observe 
that  they  gradually  approximate  towards  the  top, 
that  is,  the  north  ;  and  their  distances  increase  as  you 
proceed  towards  the  equator.  This  is  all  that  seems 
to  be  requisite  for  the  understanding  of  geographical 
charts  by  means  of  which  an  attempt  is  made  to 
represent  the  surface,  or  part  of  the  surface,  of  the 
globe. 

But  my  principal  object  was  to  demonstrate  how 
the  real  position  of  every  spot  on  the  globe  is  deter- 
mined by  its  latitude  and  longitude. 

1st  September,  1761. 


LETTER  XLV. 

Method  of  determining  the  Latitude,  or  the  Elevation 
of  the  Pole. 

IT  being  a  matter  of  such  importance  to  know  the 
latitude  and  longitude  of  every  place,  in  order  to 
ascertain  exactly  the  spot  of  the  globe  where  you 
are,  you  must  be  sensible  that  it  is  equally  important 


154  OF   DETERMINING    THE    LATITUDE. 

to  discover  the  means  of  certainly  arriving  at  such 
knowledge. 

Nothing  can  be  more  interesting  to  a  man  who 
has  been  long  at  sea,  or  after  a  tedious  journey 
through  unknown  regions,  than  to  be  informed  at 
what  precise  spot  he  is  arrived ;  whether  or  not  he 
is  near  some  known  country,  and  what  course  he 
ought  to  pursue  in  order  to  reach  it.  The  only 
means  of  relieving  such  a  person  from  his  anxiety 
would  undoubtedly  be  to  give  him  the  latitude  and 
longitude  of  the  place  where  he  is ;  but  what  must 
he  do  to  attain  this  most  important  information  ? 
Let.  us  suppose  him  on  the  ocean,  or  in  a  vast  desert, 
where  there  is  no  one  whom  he  can  consult.  After 
having  ascertained,  by  the  help  of  a  terrestrial  globe, 
or  of  maps,  the  latitude  and  longitude  of  the  place 
where  he  is,  he  will  with  ease  from  them  determine 
his  present  position,  and  be  furnished  with  the  neces- 
sary information  respecting  his  future  progress. 

I  proceed  therefore  to  inform  you  that  it  is  by 
astronomy  chiefly  we  are  enabled  to  determine  the 
latitude  and  longitude  of  the  place  where  we  are ; 
and  that  I  may  not  tire  you  by  a  tedious  detail  of  all 
the  methods  which  astronomers  have  employed  for 
this  important  purpose,  I  shall  satisfy  myself  with 
presenting  a  general  idea  of  them,  trusting  that  this 
will  be  sufficient  to  convey  to  you  the  knowledge 
of  the  principles  on  which  every  method  is  founded. 

I  begin  with  the  latitude,  which  is  involved  in 
scarcely  any  difficulty ;  whereas  the  determination 
of  the  longitude  seems  hitherto  to  have  defied  all 
human  research,  especially  at  sea,  where  the  utmost 
precision  is  requisite.  For  the  discovery  of  this 
last,  accordingly,  very  considerable  prizes  have  been 
proposed,  as  an  encouragement  to  the  learned  to 
direct  their  talents  and  their  industry  towards  a  dis- 
covery so  interesting,  both  from  its  own  importance 
and  from  the  honour  and  emolument  which  are  to 
be  the  fruit  of  it. 


OF   DETERMINING    THE    LATITUDE. 


155 


I  return  to  the  latitude,  and  the  means  of  ascer- 
taining it,  referring  to  some  future  opportunity  a 
more  ample  discussion  of  the  longitude,  and  of  the 
different  methods  of  discovering  it,  especially  at  sea. 

Let  the  points  B  and  A,  Fig.  pia-.  104. 

104,  be  the  poles  of  the  earth ; 
B  A  its  axis,  and  B  its  centre ; 
let  the  semicircle  B  D  A  repre- 
sent a  meridian,  intersected  by 
the  equator  at  the  point  D; 
and  B  D,  A  D,  will  be  each  the 
quadrant  of  a  circle,  or  an  arch 
of  90  degrees;  the  straight 
line  D  C  will  therefore  be  a  ra- 
dius of  the  equator,  and  D  E 
its  diameter. 

Let  there  now  be  assumed  in 
this  meridian  B  D  A  the  point 
L,  the  given  place  of  which  the  latitude  is  required ; 
or,  in  other  words,  the  number  of  degrees  contained 
in  the  arch  L  D,  which  measures  the  distance  of  the 
point  L  from  the  equator ;  or  again,  drawing  the 
radius  C  L,  as  the  arch  L  D  measures  the  angle 
D  C  L,  which  I  shall  call  y,  this  angle  y  will  express 
the  latitude  of  the  place  L,  which  we  want  to  find. 

Now,  it  being  impossible  to  place  ourselves  at  the 
centre  of  the  earth,  from  which  we  could  take  the 
measure  of  that  angle,  we  must  have  recourse  to  the 
heavens.  There  the  prolongation  of  the  axis  of  the 
earth  A  B  terminates  in  the  north  pole  of  the  heavens 
P,  which  we  are  to  consider  as  at  an  immense  dis- 
tance from  the  earth.  Let  the  radius  C  L  likewise 
be  carried  forward  till  it  terminate  in  the  heavens  at 
the  point  Z,  which  is  called  the  zenith  of  the  place  ; 
then,  drawing  through  the  point  L  the  straight  line 
S  T,  perpendicular  to  the  radius  C  L,  you  will  recol- 
lect that  this  line  S  T  is  a  tangent  of  the  circle,  and 
that  consequently  it  will  be  horizontal  to  the  place 


156     OF  DETERMINING  THE  LATITUDE. 

L ;  our  horizon  always  touching  the  surface  of  the 
earth  at  the  place  where  we  are. 

Let  us  now  look  from  L  towards  the  pole  of  the 
heavens  P,  which  being  infinitely  distant,  the  straight 
line  L  Q  directed  to  it  will  be  parallel  to  the  line 
A  B  P,  that  is,  to  the  axis  of  the  earth  :  this  pole  of 
the  heavens  will  appear,  therefore,  between  the  ze- 
nith and  the  horizon  L  T ;  and  the  angle  T  L  Q,  in- 
dicated by  the  letter  m,  will  show  how  much  the 
straight  line  L  Q,  in  the  direction  of  the  pole,  is  ele- 
vated above  the  horizon  ;  hence  this  angle  m  is  de- 
nominated the  elevation  of  the  pole. 

You  have  undoubtedly  heard  frequent  mention 
made  of  the  elevation  of  the  pole,  or,  as  some  call  it, 
the  height  of  the  pole ;  which  is  nothing  else  but  the 
angle  formed  by  the  straight  line  L  Q  in  the  direc- 
tion of  the  pole  and  the  horizon  of  the  place  where 
we  are.  You  have  a  perfect  comprehension  of  the 
possibility  of  measuring  this  angle  m,  by  means  of 
an  astronomical  instrument,  without  my  going  into 
any  further  detail. 

Having  measured  this  angle  m,  or  the  height  of  the 
pole,  it  will  give  you  precisely  the  latitude  of  the 
place  L,  that  is,  the  angle  y.  To  make  this  appear, 
it  is  only  necessary  to  demonstrate  that  the  two  an- 
gles m  and  y  are  equal. 

Now  the  line  L  Q  being  parallel  to  C  P,  the  angles 
m  and  n  are  alternate,  «nd  consequently  equal.  And 
the  line  L  T  being  perpendicular  to  the  radius  C  L, 
the  angle  C  L  T  of  the  triangle  C  L  T  must  be  a  right 
angle,  and  the  other  two  angles  of  that  triangle,  n 
and  a?,  must  be  together  equal  to  a  right  angle.  But 
the  arch  B  D  being  the  quadrant  of  a  circle,  the  angle 
BCD  must  likewise  be  a  right  angle  ;  the  two  angles 
x  and  y,  therefore,  are  together  equal  to  the  two 
angles  n  and  x.  Take  away  the  angle  x  from  both, 
and  there  will  remain  the  angle  y  equal  to  the  angle 
n ;  but  the  angle  n  has  been  proved  equal  to  the 


KNOWLEDGE    OF    THE   LONGITUDE.  157 

angle  m,  therefore  the  angle  y  is  likewise  equal  to 
the  angle  ra. 

It  has  already  been  remarked  that  the  angle  y  ex- 
presses the  latitude  of  the  place  L,  and  the  angle  m 
the  elevation  or  height  of  the  pole  at  the  same  place 
L ;  the  latitude  of  any  place,  therefore,  is  always 
equal  to  the  height  of  the  pole  at  that  same  place. 
The  means  which  astronomy  supplies  for  observing 
the  height  of  the  pole  indicate  therefore  the  latitude 
required. 

Astronomical  observations  made  at  Berlin  have 
accordingly  informed  us  that  there  the  height  of  the 
pole  is  52°  3#,  and  hence  we  conclude  that  the  lati- 
tude of  that  city  is  likewise  52°  32'. 

This  is  one  very  remarkable  instance  to  demon- 
strate how  the  heavens  may  assist  us  in  the  attain- 
ment of  the  knowledge  of  objects  which  relate  only 
to  the  earth. 

5th  September,  1761. 


LETTER  XLVI. 

Knowledge  of  the  Longitude,  from  a  Calculation  of  the 
Direction,  and  of  the  Space  passed  through. 

I  NOW  proceed  to  the  longitude ;  and  remark  that, 
on  taking  a  departure,  whether  by  land  or  water, 
from  a  known  place,  it  would  be  easy  to  ascertain 
the  spot  we  had  reached,  did  we  know  exactly  the 
length  of  the  road,  and  the  direction  which  we  pur- 
sued. This  might,  in  such  a  case,  be  effected  even 
without  the  aid  of  astronomy ;  and  this  obliges  me 
to  enter  into  a  more  particular  detail  on  the  subject. 

We  measure  the  length  of  a  road  by  feet ;  we 
know  how  many  feet  go  to  a  mile,  and  how  many 
miles  go  to  an  arch  of  one  degree  upon  the  globe : 
thus  we  are  enabled  to  express  in  degrees  the  dis- 
tance we  have  travelled- 

VOL.  II.  ~O 


158          KNOWLEDGE    OF    THE    LONGITUDE. 

As  to  the  route  or  direction  in  which  we  travel,  it 
is  necessary  accurately  to  know  the  position  of  the 
meridian  at  every  place  where  we  are.  As  the  me- 
ridian proceeds  in  one  direction  towards  the  north 
pole,  and  in  the  other  towards  the  south,  you  have 
only  to  draw,  on  the  horizon  of  the  spot  where  you 
are,  a  straight  line  from  north  to  south,  which  is 
called  the  meridian  line  of  that  place.  All  possible 
care  must  be  taken  to  trace  this  meridian  line  very 
accurately,  and  here  the  heavens  must  again  perform 
the  office  of  a  guide. 

^You  know  it  is  midday  when  the  sun  is  at  his 
greatest  elevation  above  the  horizon  ;  or,  which  is 
the  same  thing,  the  direction  of  the  sun  is  then  ex- 
actly south,  and  the  shadow  of  a  staff  fixed  perpen- 
dicularly on  a  horizontal  plane  will  fall,  at  that  in- 
stant, precisely  northward.  Hence  it  is  easy  to  com- 
prehend how  an  observation  of  the  sun  may  furnish 
us  with  the  means  of  accurately  tracing  a  meridian 
line,  wherever  we  may  be. 

Having  traced  a  meridian,  every  other  direction  is 
very  easily  determined. 

Let  the  straight  line  N  S,  pi.  105. 

Fig.  105,  be  the  meridian, 
one  of  the  extremities  N 
being  directed  towards  the 
north,  and  the  other  S  to- 
wards the  south.  With  this 
meridian  let  there  be  drawn 
at  right  angles  the  straight 
line  E  W,  whose  extremity 
E  shall  be  directed  towards 
the  east,  and  the  other  ex- 
tremity W  towards  the  west. 
Having  divided  the  circle 
into  sixteen  equal  parts,  we  shall  have  so  many  differ- 
ent directions,  denominated  according  to  the  letters 
affixed  to  them ;  and  in  case  of  not  pursuing  a  direc- 
tion which  exactly  corresponds  with  some  one  of  the 


KNOWLEDGE    OF    THE    LONGITUDE. 


159 


sixteen,  the  angle  must  be  marked  which  that  de- 
viating line  of  direction  makes  with  the  meridian 
N  S,  or  wrth  E  W,  which  is  perpendicular  to  it. 

It  is  thus  we  are  enabled  to  determine  exactly  the 
direction  which  we  pursue  in  travelling;  and  so 
long  as  we  are  assured  of  the  length  of  the  way,  and 
of  the  direction  pursued,  it  will  be  very  easy  to  as- 
certain the  true  place  at  which  we  have  arrived,  and 
to  indicate  both  its  longitude  and  latitude.  We  em- 
ploy for  this  purpose  an  accurate  map,  which  con- 
tains the  point  of  departure,  and  that  which  we  have 
reached  ;  and  by  means  of  the  scale,  which  gives  the 
quantity  of  miles  or  leagues  that  go  to  a  degree,  it  is 
easy  to  trace,  on  such  map,  the  track  pursued  and 
completed. 

Fig.  106  represents  a  map,  on  which  are  marked 
from  left  to  right  the  degrees  of  longitude,  and  those 
Fig.  106. 


13     14-    15    16    17     18    Iff    20   2J   22 


24   25    20 


15     JL6      IT     18     JL9     20     21     22     23     2+    25 


160  KNOWLEDGE    OP   THE   LONGITUDE. 

of  latitude  from  top  to  bottom  ;  it  is  likewise  visible 
on  the  face  of  it,  that  the  meridians  converge  as 
they  approach  towards  the  north,  and  retire  from 
each  other  towards  the  south,  as  is  the  actual  case 
on  the  globe. 

This  map  contains  part  of  the  surface  of  the  earth, 
from  the  53d  degree  of  north  latitude  to  the  59th  de- 
gree ;  and  from  the  13th  degree  of  longitude  to  the 
26th. 

Suppose,  then,  I  take  my  departure  from  the  place 
L,  the  longitude  of  which  is  16°,  and  the  latitude 
57°  20',  and  that  I  proceed  in  the  direction  E  S  E, 
and  have  travelled  a  space  of  345  English  miles.  In 
order  to  determine  the  longitude  and  latitude  of  the 
place  I  have  reached,  I  draw  from  the  place  L  the 
straight  line  L  M,  making  with  the  meridian  an  angle 
of  67°  30',  the  same  angle  which  the  direction  E  S  E 
in  the  preceding  figure  makes  with  N  S.  Then  on 
that  line  I  take,  according  to  the  scale  marked  on 
the  chart,  L  M  equal  to  345  English  miles,  and  the 
point  M  shall  be  the  place  which  I  have  reached. 

I  have  then  only  to  compare  this  place  with  the 
meridians  and  parallels  traced  on  the  map,  and  I  find 
that  its  longitude  is  24°  nearly ;  and  on  measuring 
more  exactly  the  part  of  the  degree  to  be  added  to 
the  24th  degree,  I  find  the  longitude  of  the  point  M 
to  be  24°  4'.  As  to  the  latitude,  I  observe  it  to  be 
between  the  55th  and  56th  degree,  and  by  an  easy 
computation  I  find  it  to  be  55°  25' ;  so  that  the  lati- 
tude of  the  place  M,  which  1  have  reached,  is  55° 
25',  and  its  longitude  24°  4'. 

It  has  here  been  supposed  that  I  have  invariably 
pursued  the  same  direction,  E  S  E,  from  first  to  last ; 
but  if  I  have  from  time  to  time  deviated  from  that 
direction,  I  have  only  to  perform  the  same  opera- 
tion on  each  deviation,  to  find  the  place  where  I  then 
was  ;  from  this  I  take  a  fresh  departure,  and  trace 
my  direction  till  another  deviation  takes  place ;  and 
so  on,  till  I  reach  my  object.  By  these  means  it  is 
always  in  my  power,  whether  travelling  by  sea  or 


KNOWLEDGE    OF    THE    LONGITUDE.  161 

land,  to  ascertain  the  place  I  have  reached  ;  provided 
I  know  exactly,  through  my  whole  progress,  the 
direction  I  pursue,  and  measure  with  equal  accuracy 
the  length  of  the  way. 

We  might  in  this  case  dispense  even  with  the  as- 
sistance  of  astronomy,  unless  we  had  occasion  for  it 
accurately  to  determine  our  direction,  or  the  angle 
which  it  makes  with  the  meridian ;  but  the  magnetic 
needle  or  compass  may,  in  many  cases,  supply  this 
want. 

You  must  be  sensible,  however,  that  it  is  possible 
to  make  a  very  considerable  mistake,  both  in  the 
computation  of  the  direction  and  of  the  length  of  the 
way,  especially  in  very  long  voyages.  How  often 
is  it  necessary  to  change  the  direction  in  travelling 
even  from  hence  to  Magdeburg  ?  and  how  is  it  possi- 
ble to  measure  exactly  the  length  of  the  way  ?  But 
when  we  travel  by  land  we  are  not  reduced  to  this 
expedient ;  for  we  are  enabled  to  measure  by  geo- 
metrical experiments  the  distance  of  places,  and  the 
angles  which  the  distances  make  with  the  meridian 
of  every  place ;  and  thus  we  can  determine,  with 
tolerable  accuracy,  the  true  situation  of  all  places. 

8th  September,  1761. 


LETTER  XLVII. 

Continuation.     Defects  of  this  Method. 

A  METHOD  of  observing  the  direction  pursued  and 
the  length  of  the  course,  seems  to  be  of  singular 
utility  in  sea  voyages,  because  there  we  are  not 
under  the  necessity  of  deviating  from  the  direction 
every  moment,  as  in  travelling  by  land ;  for  with  the 
same  wind  we  can  proceed  in  the  same  direction. 

Pilots  are  accordingly  very  attentive  in  exactly 
observing  the  course  of  the  vessel,  and  in  measuring 
the  progress  she  has  made.  They  keep  an  accurate 
O  2 


162  KNOWLEDGE    OF    THE    LONGITUDE. 

journal  of  all  these  observations  at  the  close  of  every 
day,  nay  still  more  frequently ;  they  trace  on  their 
sea-charts  the  progress  they  have  made,  and  thus 
are  enabled  to  mark  on  the  charts,  for  every  period 
of  time,  the  point  where  they  are  *and  of  which  they 
consequently  know  the  latitude  and  longitude.  Ac- 
cordingly, so  long  as  the  course  is  regular,  and  the 
vessel  is  not  agitated  by  a  tempest,  good  pilots  are 
seldom  mistaken ;  but  when  they  are  in  doubt,  they 
have  recourse  to  astronomical  observations,  from 
which  they  discover  the  elevation  of  the  pole ;  and 
this  being  always  equal  to  the  latitude  of  the  place 
where  they  are,  they  compare  it  with  that  which 
they  have  marked  on  the  chart,  conformably  to  the 
computation  of  their  progress.  If  these  are  found  to 
coincide,  their  computation  is  just ;  if  they  discover 
a  difference,  they  conclude  with  certainty  that  some 
error  has  been  committed  in  the  computation  of  the 
distance  and  of  the  course  ;  in  that  case  they  re-ex- 
amine both  the  one  and  the  other  more  carefully, 
and  endeavour  to  apply  the  necessary  corrections, 
in  order  to  make  the  computation  agree  with  the 
observation  of  the  height  of  the  pole,  or  of  the  lati- 
tude, which  is  equal  to  it. 

This  precaution  may  be  sufficient  in  short  voyages, 
as  the  errors  committed  can  in  these  be  of  no  great 
importance ;  but  in  very  long  voyages,  these  slight 
mistakes  may  accumulate  to  such  a  degree  that  at 
last  a  very  gross  mistake  may  be  committed,  and 
the  place  where  the  vessel  actually  is  may  differ 
considerably  from  what  it  was  supposed  to  be  on 
the  chart. 

I  have  hitherto  gone  on  the  supposition  that  the 
voyage  proceeded  quietly ;  but  should  a  storm  arise, 
during  which  the  vessel  is  subjected  to  the  rudest 
concussions  of  wind  and  waves,  it  is  evident  that 
the  computation  of  distance  and  course  is  entirely 
deranged,  and  that  it  is  impossible  to  trace  on  the 
chart  the  progress  she  has  made. 


KNOWLEDGE    OF    THE    LONGITUDE.  163 

It  would  be  very  easy  after  this  derangement  to 
ascertain  by  astronomical  observations  the  latitude 
of  the  ship's  place ;  but  this  would  determine  only 
the  parallel  of  that  place,  and  it  would  remain 
totally  uncertain  at  what  point  of  the  parallel  she 
actually  was. 

It  is  necessary  therefore  to  discover  likewise  the 
longitude  of  the  place,  which  shows  us  the  meridian 
under  which  it  is  situated ;  and  then  the  intersection 
of  that  meridian  with  the  parallel  found  will  give 
the  vessel's  true  place.  This  will  make  you  sensi- 
ble of  what  importance  it  is  to  assist  mariners  in 
discovering  likewise  the  longitude  of  the  place  where 
they  are. 

This  necessity  is  imposed  not  only  from  the  con- 
sideration of  the  tempests  to  which  navigation  is 
liable;  for  it  is  possible,  supposing  the  voyage  to 
proceed  ever  so  quietly,  to  be  grossly  mistaken  in 
the  computation  of  both  course  and  distance.  Could 
we  suppose  the  sea  to  be  at  rest,  it  might  be  pos- 
sible to  invent  various  methods  of  ascertaining  with 
tolerable  exactness  the  way  which  the  vessel  has 
made ;  but  there  are  rapid  currents  in  many  places 
of  the  ocean,  which  have  the  resemblance  of  a  river 
running  in  a  certain  direction.  Thus  it  is  observed 
that  the  Atlantic  Ocean  has  a  perpetual  current 
into  the  Mediterranean  Sea.  through  the  Straits  of 
Gibraltar ;  and  that  the  ocean  between  Africa  and 
America  has  a  very  considerable  current  from  east 
to  west,  so  that  a  voyage  to  America  is  performed 
in  much  less  time  than  a  voyage  from  America  to 
Europe. 

Were  such  currents  constant  and  well  known,  we 
should  have  considerable  assistance  towards  form- 
ing our  calculations ;  but  it  has  been  observed  that 
they  are  sometimes  more,  sometimes  less  rapid,  and 
that  they  frequently  change  their  direction ;  which 
deranges  the  calculations  of  the  most  skilful  navi- 
gator to  such  a  degree  that  it  is  no  longer  safe  to 


164  KNOWLEDGE    OF    THE    LONGITUDE. 

trust  them.  We  have  but  too  many  fatal  instances 
of  ships  dashed  on  concealed  rocks  and  lost,  because 
these  were  computed  to  be  still  at  a  considerable 
distance.  It  was  afterward  discovered,  when  too 
late,  that  these  calamities  had  been  occasioned  by 
the  currents  of  the  ocean,  which  deranged  the  cal- 
culations of  navigators. 

In  fact,  when  the  ocean  has  a  current  which  makes 
it  flow  like  a  river,  following  a  certain  direction, 
vessels  caught  in.it  are  carried  away  imperceptibly. 
In  a  river  we  clearly  perceive  that  the  current  is 
carrying  us  along,  by  observing  the  banks  or  the 
bottom ;  but  at  sea  no  land  is  visible,  and  the  depth 
is  too  great  to  admit  of  our  making  any  observation 
from  the  bottom.  At  sea,  then,  it  is  impossible 
to  discern  the  currents  ;  and  hence  so  many  dread- 
ful mistakes  respecting  both  course  and  distance. 
Whether,  therefore,  we  take  tempests  into  the  ac- 
count or  not,  we  are  always  under  the  necessity  of 
falling  on  other  methods  of  ascertaining  the  longi- 
tude of  the  places  where  we  may  arrive  ;  and  of  the 
various  methods  hitherto  employed  for  acquiring 
this  knowledge  of  the  longitude  I  now  proceed  to 
inform  you. 

12th  September,  1761. 


LETTER  XLVIII. 

Second  Method  of  determining  the  Longitude,  by  means 
of  an  exact  Timepiece. 

A  VERY  sure  method  of  finding  the  longitude  would 
be  a  clock,  watch,  or  pendulum,  so  perfect,  that  is 
to  say,  which  should  always  go  so  equally  and  so 
exactly,  that  no  concussion  should  be  able  to  affect 
its  motion. 

Supposing  such  a  timepiece  constructed,  let  us 
see  in  what  manner,  by  means  of  it,  we  should  be 


KNOWLEDGE    OF    THE    LONGITUDE.  165 

enabled  to  solve  the  problem  of  the  longitude.  We 
must  return,  for  this  purpose,  to  the  consideration 
of  meridians,  which  we  are  to  conceive  to  be  drawn 
through  every  place  on  the  surface  of  the  globe. 

You  know  that  the  sun  seems  to  describe  every 
day  a  circle  round  the  earth,  and  that,  of  conse- 
quence, he  passes  successively  over  all  the  meridians 
in  the  space  of  twenty-four  hours. 

Now,  the  sun  is  said  to  pass  over  or  through  a 
given  meridian,  if  a  straight  line  drawn  from  the  sun 
to  the  centre  of  the  earth  C,  Fig.  107,   p.     ^ 
pass  precisely  through  that  meridian.        »" 
If,  therefore,  in  the  present  case  the 
line  drawn  from  the  sun  to  the  centre  of 
the  earth  pass  through  the  meridian 
B  L  M  A,  we  would  say  that  the  sun 
was  in  that  meridian,  and  then  it  would 
be  midday  to  all  the  places   situated 
under  this  meridian  ;  but  under  every  other  it  would 
not  be  midday  at   that  precise   instant;   it  would 
there  be  before  noon  or  after  it  everywhere  else. 

If  the  meridian  B  N  A  is  situated  to  the  east- 
ward of  the  meridian  B  M  A,  the  sun,  in  making  his 
circuit  from  east  to  west,  must  pass  over  the  meri- 
dian B  N  A  before  he  reaches  the  meridian  B  M  A ; 
consequently  it  will  be  midday  under  the  meridian 
B  N  A  earlier  than  under  the  meridian  B  M  A ; 
when,  therefore,  it  shall  be  midday  under  this  last 
meridian,  midday  under  every  other  meridian  to  the 
eastward  will  be  already  past,  or  it  will  be  afternoon 
with  them.  On  the  contrary,  it  will  be  still  fore- 
noon under  every  meridian,  say  B  D  A,  situated  to 
the  westward,  as  the  sun  cannot  reach  it  till  he  has 
passed  over  the  meridian  B  M  A. 

And  as  the  motion  of  the  sun  is  regular  and  uni- 
form, and  he  completes  his  circuit  of  the  globe,  that 
is  360  degrees,  in  twenty-four  hours,  he  must  every 
hour  describe  an  arch  of  15  degrees.  When,  there- 
fore, it  is  noon  at  Berlin,  and  at  every  other  place 
situated  under  the  same  meridian,  noon  will  be 


166  KNOWLEDGE    OF    THE    LONGITUDE. 

already  past  under  meridians  situated  to  the  eastward ; 
and  more  particularly  still  under  the  meridian  situ- 
ated 15  degrees  to  the  eastward  of  that  of  Berlin,  it 
will  already  be  one  o'clock  ;  under  the  meridian  30 
degrees  eastward,  two  o'clock ;  under  that  of  45  de- 
grees, three  o'clock  afternoon,  and  so  on.  The  con- 
trary will  take  place  under  meridians  situated  to  the 
westward  of  that  of  Berlin  ;  when  it  is  noon  there,  it 
will  be  only  eleven  o'clock  forenoon  under  the  me- 
ridian 15  degrees  to  the  westward,  ten  o'clock  under 
the  meridian  of  30,  nine  o'clock  under  the  meridian 
of  45  degrees  westward,  and  so  on ;  •  a  difference  of 
15  degrees  between  two  meridians  always  amounting 
to  an  hour  of  time. 

To  elucidate  still  more  clearly  what  has  now  been 
remarked,  let  us  compare  the  two  cities  Berlin  and 
Paris.  As  the  meridian  of  Berlin  is  11°  17'  15"  to 
the  eastward  of  that  of  Paris,  reckoning  an  hour  to 
15  degrees,  this  difference  of  11°  17'  15"  will  give  44 
minutes  and  29  seconds  of  time,  or  three-quarters 
of  an  hour  nearly.  When,  therefore,  it  is  midday 
at  Paris,  it  will  be  44  minutes  and  29  seconds  after 
midday  at  Berlin ;  and  reciprocally,  when  it  is  mid- 
day at  Berlin,  it  will  only  be  15  minutes  and  31  sec- 
onds after  eleven  o'clock  at  Paris ;  so  that  it  will 
not  be  noon  at  this  last  city  till  44  minutes  and  29 
seconds  afterward.  Hence  it  is  evident,  that  the 
clocks  at  Berlin  should  always  be  faster  than  those 
of  Paris,  and  that  this  difference  ought  to  be  nearly 
44  minutes  and  29  seconds. 

The  difference  between  the  meridians  of  Berlin 
and  Magdeburg  is  nearly  1°  40' ;  Berlin  therefore  is 
to  the  eastward  of  Magdeburg ;  and  this  difference 
reduced  to  time  gives  6  minutes  and  40  seconds, 
which  the  clocks  of  Berlin  ought  to  indicate  more 
than  that  of  Magdeburg.  Consequently,  if  it  is  just 
now  noon  at  Magdeburg,  and  the  clocks  there,  which 
I  suppose  well  regulated,  point  to  XII.,  the  clocks 
at  Berlin  should,  at  the  same  instant,  indicate  6 


KNOWLEDGE    OF    THE    LONGITUDE.  167 

minutes  and  40  seconds  after  XII.,  that  is,  noon 
there  is  already  past. 

Hence  you  see,  that  in  proportion  as  places  differ 
in  longitude,  or  as  they  are  situated  under  different 
meridians,  well-regulated  timepieces  ought  not  to 
point  out  the  same  hour  at  the  same  instant,  but  the 
difference  ought  to  be  a  whole  hour  when  that  of 
the  longitude  is  15  degrees. 

In  employing  a 'timepiece,  then,  for  ascertaining 
the  longitude  of  the  places  through  which  we  pass, 
it  would  first  be  necessary  to  regulate  it  exactly  at 
some  place  where  we  actually  were.  This  is  done 
by  observing  the  instant  of  noon,  that  is,  the  instant 
when  the  sun  passes  over  the  meridian  of  that  place ; 
and  the  timepiece  ought  then  to  point  precisely  to 
XII.  It  ought  afterward  to  be  adjusted  in  such  a 
manner,  that  always  after  a  revolution  of  24  hours, 
when  the  sun  returns  to  the  meridian,  the  index  after 
having  made  two  complete  circuits,  should  again 
point  exactly  to  XII.  If  this  is  carefully  observed, 
such  well  regulated  timepieces  will  not  coincide  in 
different  places,  unless  tii«?se  be  situated  under  one 
and  the  same  meridian ;  but  if  they  are  situated  under 
different  meridians,  that  is,  if  there  be  a  difference 
of  longitude,  the  time  indicated  by  the  clock  or 
watch,  at  the  same  moment,  will  likewise  be  differ- 
ent ;  at  the  rate  of  one  whole  hour  of  time  for  every 
15  degrees  of  longitude. 

Knowing,  then,  the  difference  of  time  indicated 
by  well  regulated  timepieces,  at  different  places, 
and  at  the  same  instant,  we  are  enabled  exactly  to 
compute  the  difference  of  longitude  at  these  two 
places,  reckoning  always  15  degrees  for  an  hour, 
and  the  fourth  part  of  a  degree  for  a  minute. 
15J/4  September,  1761. 


168  KNOWLEDGE    OF    THE    LONGITUDE. 

LETTER  XLIX. 

Continuation)  and  further  Elucidations. 

You  will  be  less  surprised  at  the  difference  of  time 
which  well  regulated  timepieces  must  indicate  under 
different  meridians,  when  you  recollect,  that  while 
it  is  noon  with  us,  there  are  countries  towards  the 
east  where  the  sun  is  already  set,  and  that  there  are 
others  towards  the  west  where  he  is  but  just  rising. 
It  must  therefore  be  already  night  with  the  one,  and 
still  morning  with  the  other,  at  the  same  instant  that 
it  is  noon  with  us.  You  know,  besides,  that  with 
our  antipodes,  who  are  under  the  meridian  diametri- 
cally opposite  to  ours,  it  is  night,  while  it  is  day  with 
us ;  so  that  our  noon  corresponds  exactly  to  their 
midnight. 

It  will  be  an  easy  matter,  after  these  elucidations, 
to  show  how  an  exact  timepiece  may  assist  us  in 
discovering  the  difference  ol"  meridians,  or  that  of  the 
longitude,  at  different  places. 

Supposing  me  possessed  of  such  an  excellent  time- 
piece, which,  once  exactly  regulated,  shows  me  every 
day  the  precise  time  it  is  at  Berlin,  so  that  whenever 
it  is  noon  at  Berlin,  it  points  precisely  to  XII.:  sup- 
posing further,  that  it  goes  so  regularly,  that  once 
adjusted,  I  have  no  further  occasion  to  touch  it,  and 
that  its  motion  is  not  to  be  deranged  either  by  the 
shaking  of  a  carriage,  or  the  agitation  of  a  vessel 
on  the  ocean,  or  by  any  concussion  whatever  to  which 
it  may  be  exposed. 

Provided  thus  with  a  timepiece  of  this  descrip- 
tion,  I  set  out  to  travel,  whether  by  land  or  by  sea ; 
perfectly  assured,  that  go  where  I  will,  its  motion 
will  be  steady  and  uniform,  as  if  I  had  remained  at 
Berlin :  it  will  every  day  point  to  XII.  at  the  very 
moment  it  is  noon  at  Berlin,  and  that  wherever  I 


KNOWLEDGE    OF    THE    LONGITUDE.  169 

may  happen  to  be.  On  this  journey,  I  arrive  first 
at  Magdeburg:  there  I  observe  the  sun  when  he 
/passes  the  meridian,  and  this  happens  when  he  is 
exactly  south  ;  and  it  being  then  noon  at  Magdeburg, 
I  consult  my  timepiece,  and  observe  it  points  to  6 
minutes  and  40  seconds  after  XII. :  whence  I  con- 
clude, that  when  it  is  noon  at  Magdeburg,  noon  at 
Berlin  is  already  past,  and  that  the  difference  is 
6'  40"  of  time,  which  correspond  to  1°  40'  of  distance  ; 
therefore  the  meridian  of  Magdeburg  is  to  the  west- 
ward of  that  of  Berlin.  The  longitude  of  Berlin, 
therefore,  being  nearly  31°  7'  15',  the  longitude  of 
Magdeburg  will  be  1°  40'  less,  that  is,  it  will  be  29° 
27'  15". 

I  thence  proceed  to  Hamburgh,  accompanied  by 
my  timepiece,  which  I  never  touch ;  and  there  ob- 
serving when  it  is  noon  by  the  sun,  for  I  cannot 
depend  on  the  public  clocks  which  there  announce 
the  hour,  I  find  my  timepiece  already  announces 
13'  33''  after  XII. ;  so  that  at  Berlin  noon  is  past 
13'  33"  when  it  is  exactly  noon  at  Hamburgh:  hence 
I  conclude,  that  the  meridian  of  Hamburgh  is  3°  23' 
15"  to  the  westward  of  that  of  Berlin ;  reckoning  15° 
to  an  hour,  that  is  one  degree  for  every  four  minutes 
of  time :  accordingly,  I  find  that  13'  33"  of  time  give 
3°  23'  15''  of  distance  for  the  difference  of  the  me- 
ridians. The  longitude  of  Hamburgh  will  be  of  course 
27°  44'. 

At  Hamburgh  I  go  to  sea,  still  accompanied  by  my 
timepiece,  and  after  a  long  voyage  I  arrive  at  a  place 
where,  waiting  for  noon,  the  moment  of  which  I  ascer- 
tain by  observing  the  sun,  I  find  that  my  timepiece 
indicates  only  58'  15"  after  X. ;  so  that  then  it  is  not 
yet  noon  at  Berlin,  and  the  difference  of  time  is  1  hour 
1  minute  and  45  seconds,  from  which  I  conclude,  that 
the  place  at  which  I  have  arrived  is  to  the  eastward  of 
Berlin ;  and  as  one  hour  gives  15  degrees,  one  minute 
of  time  15',  and  45  seconds  of  time  11'  15",  the  differ- 
ence of  the  meridians  will  therefore  be  15°  26'  15' . 

tfoL.   II  — P 


170  KNOWLEDGE    OF    THE    LONGITUDE. 

I  find,  then,  that  I  am  at  a  place  to  the  eastward  of 
Berlin,  whose  longitude  is  greater  than  that  of  Berlin 
by  15°  26'  15" ;  now  the  longitude  of  that  city  being 
nearly  31°  7'  15",  the  longitude  of  the  place  where  I 
am  must  be  46°  33'  30".  Thus  I  have  discovered 
under  what  meridian  I  now  am ;  but  I  am  still  un- 
certain as  to  the  point  of  the  meridian.  In  order  to 
ascertain  this,  I  have  recourse  to  astronomical  obser- 
vations, and  find  the  height  of  the  pole  to  be  precisely 
41°.  Knowing  likewise  that  I  am  still  in  the  north- 
ern hemisphere,  as  I  have  not  passed  the  equator,  I 
discover  that  I  actually  am  at  a  place  whose  latitude 
is  41°  north,  and  longitude  46°  33'  30".  I  take  there- 
fore my  globe  or  maps,  and  trace  the  meridian  whose 
longitude  is  46°  33'  30" ;  I  look  for  the  place  whose 
latitude  is  41°,  and  at  the  point  of  intersection  I  find 
I  have  got  to  the  city  of  Constantinople  without 
having  occasion  to  apply  for  information  to  any  per- 
son whatever. 

Thus,  at  whatever  place  of  the  globe  I  may  arrive, 
possessed  of  a  timepiece  so  exact,  I  am  able  to 
ascertain  the  longitude  of  it ;  and  then  an  observation 
of  the  height  of  the  pole  will  show  me  its  latitude. 
All  that  remains,  therefore,  is  to  take  the  terrestrial 
globe,  or  a  good  map,  and  it  will  be  easy  for  me  to 
ascertain  where  I  am,  however  unknown  to  me  the 
country  may  in  other  respects  be. 

It  is  much  to  be  regretted,  that  artists  of  the 
greatest  ability  have  hitherto  been  unsuccessful  in 
the  construction  of  timepieces  such  as  I  have  de- 
scribed, and  such  as  the  case  requires.  We  meet 
with  a  great  many  very  good  pendulum  machines, 
but  they  go  regularly  only  when  fixed  in  undisturbed 
situations ;  the  slightest  concussion  is  apt  to  derange 
their  motion ;  they  are  therefore  totally  useless  in 
long  sea  voyages.  It  is  obvious  that  the  pendulum, 
which  regulates  the  motion,  is  incapable  of  resisting- 
the  shocks  to  which  it  is  exposed  in  navigation. 
About  ten  years  ago,  however,  an  English  artist 
pretended  that  he  had  constructed  a  timepiece  proof 


KNOWLEDGE    OF    THE    LONGITUDE.  171 

against  the  motion  of  a  ship  at  sea,  and  that  after 
having  tried  it  a  long  time  together  in  a  carriage  on 
the  road,  it  was  impossible  to  perceive  the  slightest 
derangement ;  on  which  the  inventor  claimed  and 
received  part  of  the  parliamentary  reward  proposed 
for  the  discovery  of  the  longitude,  and  the  rest  was 
to  be  paid  after  it  had  been  put  to  the  proof  of  a 
long  voyage.  But  since  that  time  we  have  heard  no 
more  of  it ;  from  which  it  is  to  be  presumed  that 
this  attempt  too  has  failed,  like  many  others  which 
had  the  same  object  in  view.* 
19th  September,  1761. 


LETTER  L. 

Eclipses  of  the  Moon,  a  third  Method  of  finding  the 
Longitude. 

FROM  want  of  the  exquisite  timepiece  of  which  I 
have  endeavoured  to  give  you  an  idea,  the  eclipses 
of  the  moon  have  hitherto  been  considered  as  the 
most  certain  method  of  discovering  the  longitude ; 
but  these  phenomena  present  themselves  so  rarely, 

*  TUe  attempt  has  by  no  means  failed.  The  reward  offered  by  the 
French  Academy,  and  more  especially  the  liberal  reward  offered  by  the 
British  parliament  of  20,0001.,  for  a  discovery  that  should  determine  the 
longitude  within  half  a  degree,  provided  such  method  should  extend  more 
than  80  miles  from  the  coast,  stimulated  the  ingenuity  of  various  me- 
chanicians, and  led  to  the  discovery  of  several  means  by  which  the  ex- 
pansion and  contraction  of  metals  by  heat  and  cold  (the  principal  cause 
of  irregularity  in  the  best  timekeepers)  were  very  nearly  compensated, 
and  an  equable  motion  established.  The  large  reward  of  20,000/.  was 
gained  by  Harrison,  for  his  invention  of  the  gridiron  pendulum,  and  the 
application  of  the  same  principle  to  a  watch  to  effect  a  self-regulating  curb 
for  limiting  the  effective  length  of  the  spiral  pendulum  spring.  This 
reward,  which  it  is  said  was  actually  increased  by  gratuities  of  the  Board 
of  Longitude,  the  East  India  Company,  and  others,  to  24.000Z.,  was  paid  to 
James  and  William  Harrison,  father  and  son,  in  1774,  and  a  new  act  of 
parliament  was  passed,  granting  further  but  less  rewards  for  still  "reater 
perfection  in  the  construction  of  chronometers.  By  the  successive  labours 
of  Mudge,  Arnold,  Earnshaw,  and  others,  the  art  of  chronometer  making 
ias  been  brought  to  so  great  perfection,  as  to  render  this  instrument  of 
the  highest  value  to  the  navigator,  and  to  bring  it  within  the  reach  of 
almost  every  ship-master. — Am.  Ed 


172  KNOWLEDGE    OF   THE    LONGITUDE. 

that  we  have  it  not  in  our  power  to  employ  them  so 
often  as  occasion  requires. 

You  know  that  the  moon  is  eclipsed  when  it 
passes  into  the  shadow  of  the  earth :  it  is  possible 
then  to  observe  the  moment  when  the  moon  begins 
to  enter  into  the  shade,  and  when  she  has  emerged ; 
the  one  is  denominated  the  beginning  of  the  eclipse, 
and  the  other  its  end ;  and  when  both  are  observed, 
the  mean  time  between  them  is  denominated  the 
middle  of  the  eclipse.  The  moon  is  sometimes 
wholly  immerged  in  the  shadow  of  the  earth,  and 
remains  for  some  time  invisible ;  this  we  call  a  total 
eclipse,  during  which  we  may  remark  the  moment 
when  the  moon  entirely  disappears,  and  that  when 
she  begins  to  emerge ;  the  former  is  called  the 
beginning  of  total  darkness,  and  the  latter  the  end  of 
it.  But  when  a  part  only  of  the  moon  is  obscured, 
we  call  it  a  partial  eclipse ;  and  we  can  remark  only 
the  moment  of  its  beginning  and  ending.  You  know 
likewise  that  eclipses  of  the  moon  can  happen  only 
at  the  full,  and  that  but  rarely. 

When,  therefore,  an  eclipse  of  the  moon  is  ob- 
served at  two  different  places  situated  under  different 
meridians,  the  beginning  of  the  eclipse  will  be  clearly 
seen  at  both,  and  at  the  same  instant ;  but  the  time- 
pieces at  these  different  places  will  by  no  means 
indicate  the  same  hour,  or  any  other  division  of  time 
exactly  the  same  :  I  mean  well  regulated  timepieces, 
each  of  which  points  precisely  to  XII.  when  it  is 
noon  at  that  place.  If  these  places  are  situated 
under  the  same  meridian,  their  timepieces  will  no 
doubt  indicate  the  same  time  at  the  beginning  and 
at  the  end  of  the  eclipse.  But  if  these  two  meridians 
are  15  degrees  distant  from  each  other,  that  is,  if 
the  difference  of  their  longitude  be  15°,  the  time- 
pieces must  differ  a  complete  hour  from  the  begin- 
ning to  the  end  of  the  eclipse ;  the  timepiece  of  the 
place  situated  to  the  eastward  will  indicate  one  hour 
more  than  the  other :  the  difference  of  30°  in  longi- 


KNOWLEDGE    OF    THE    LONGITUDE. 


173 


tude  will  occasion  that  of  two  hours  in  the  time  indi- 
cated by  well  regulated  clocks  or  watches  ;  and  so 
on,  according  to  the  following  table  : 


DIFFERENCE   OF   LONGITUDE. 

DIFFERENCE    OF    LONGITUDE. 

Of  Degrees. 

Of  Time. 

Of  Degrees. 

Of  Time. 

15° 

1  Hour. 

105 

7  Hours. 

30 

2 

120 

8 

45 

3 

135 

9 

60 

4 

150 

10 

75 

5 

165 

11 

90 

6 

180 

12 

If,  therefore,  the  difference  of  the  longitude  were 
150°,  the  timepieces  would  differ  ten  hours  from  the 
beginning  to  the  end  of  the  eclipse. 

Thus,  when  the  same  eclipse  is  observed  at  two 
different  places,  and  the  moment  of  its  commence- 
ment is  exactly  marked  on  the  timepieces  at  each, 
it  will  be  easy  to  calculate  from  the  difference  of  the 
time  indicated,  the  difference  of  longitude  between 
the  two  places.  Now,  that  where  the  time  is  more 
advanced  must  be  situated  more  towards  the  east, 
and  consequently  its  longitude  greater,  as  longitude 
is  reckoned  from  west  to  east. 

By  such  means,  accordingly,  the  longitude  of  the 
principal  places  on  the  globe  have  been  determined, 
and  geographical  charts  are  constructed  conformably 
to  these  determinations.  But  it  is  always  necessary 
to  compare  the  observations  made  in  a  place  the 
longitude  of  which  was  not  already  known,  with 
those  which  had  been  made  in  a  known  place,  and 
to  wait  the  result  of  that  comparison.  Were  I  to 
arrive,  then,  after  a  long  voyage,  at  an  unknown 
place,  and  an  opportunity  presented  itself  of  there 
observing  an  eclipse  of  the  moon,  this  would,  in  the 
first  instance,  afford  me  no  assistance  towards  the 
P2 


174  KNOWLEDGE    OF    THE    LONGITUDE. 

discovery  of  the  longitude  of  that  place  ;  I  could 
not,  till  after  my  return,  compare  my  observation 
with  another  made  in  a  known  place,  and  thus  I 
should  learn  too  late  where  I  was  at  that  time.  The 
grand  point  in  request  is,  How  am  I  at  the  moment 
to  acquire  the  necessary  information,  that  I  may 
take  my  measures  accordingly  1 

Now,  the  motion  of  the  moon  being  so  exactly 
known,  it  is  possible  to  attain  this  satisfaction ;  for 
we  are  thereby  enabled,  not  only  to  calculate  before- 
hand all  future  eclipses,  but  to  ascertain  the  moment 
of  the  beginning  and  end,  according  to  the  time- 
pieces of  a  given  place.  You  know  that  our  Berlin 
almanacs  always  indicate  the  beginning  and  the 
end  of  every  eclipse  visible  at  that  city.  In  the 
view,  then,  of  undertaking  a  long  voyage,  I  can  fur- 
nish myself  with  a  Berlin  almanac ;  and  if  an  op- 
portunity presents  itself  of  observing  an  eclipse  of 
the  moon  at  an  unknown  place,  I  must  mark  exactly 
the  time  of  it  by  a  timepiece  accurately  regulated 
by  the  sun  at  noon,  and  compare  the  moments  of  the 
beginning  and  end  of  the  eclipse  with  those  indicated 
in  the  almanac,  in  order  to  ascertain  the  difference 
between  the  meridian  of  Berlin  and  that  which 
passes  through  the  place  where  I  am. 

But  besides  the  rarity  of  eclipses  of  the  moon, 
this  method  is  subject  to  a  further  inconvenience ; 
we  are  not  always  able  to  distinguish  with  sufficient 
accuracy  the  moment  of  the  beginning  and  end  of 
the  eclipse,  which  comes  on  so  imperceptibly  that  a 
mistake  of  several  seconds  may  very  easily  be  com- 
mitted. But  as  the  mistake  will  be  nearly  the  same 
at  the  end  as  at  the  beginning,  we  calculate  the 
middle  point  of  time  between  the  two  moments  ob- 
served, which  will  be  that  of  the  eclipse ;  and  we 
afterward  compare  this  with  that  which  is  indicated 
by  the  almanac  for  Berlin,  or  for  any  other  known 
place. 

If  the  almanac  for  next  year  should  not  be  pub- 


KNOWLEDGE    OF   THE    LONGITUDE.  175 

lished  when  I  set  out  on  my  voyage,  or  supposing-  it 
to  last  more  years  than  one,  there  are  books  con- 
taining the  eclipses  calculated  for  several  years  to 
come. 
22d  September,  1761. 


LETTER  LI. 

Observation  of  the  Eclipses  of  the  Satellites  of  Jupiter, 
a  fourth  Method  of  finding  the  Longitude. 

ECLIPSES  of  the  sun  may  likewise  assist  in  ascer- 
taining the  longitude,  but  in  a  way  that  requires 
more  profound  research,  because  the  sun  is  not  im- 
mediately obscured ;  it  is  only  the  interposition  of 
the  body  of  the  moon  which  obstructs  the  trans- 
mission of  his  rays  to  us,  as  when  we  employ  a 
parasol  to  shelter  us  from  them,  which  does  not  pre- 
vent others  from  beholding  all  their  lustre.  For  the 
moon  conceals  the  sun  only  from  part  of  the  inhabit- 
ants of  the  earth ;  and  an  eclipse  of  the  sun  may 
be  clearly  visible  at  Berlin,  while  at  Paris  there  is 
no  interception  of  his  light. 

But  the  moon  is  really  eclipsed  by  the  shadow  of 
the  earth;  her  own  light  is  diminished  or  extin- 
guished by  it :  hence  the  eclipses  of  the  moon  are 
seen  in  the  same  manner  wherever  she  is  above  the 
horizon  at  the  time  of  the  eclipse. 

It  cannot  have  escaped  your  penetration,  that  if 
there  were  other  heavenly  bodies  which  from  time 
to  time  underwent  any  real  obscuration,  they  might 
be  employed  with  similar  success  as  the  eclipses  of 
the  moon  in  ascertaining  the  longitude.  The  satel- 
lites of  Jupiter,  which  pass  so  frequently  into  the 
shadow  of  their  planet  that  almost  every  night  one 
or  other  of  them  is  eclipsed,  may  be  ranked  in  the 
number  of  these,  and  furnish  us  with  another  excel- 


176 


KNOWLEDGE    OF    THE    LONGITUDE. 


Fig.  108. 


lent  method  of  determining  the  longitude.     Astrono- 
mers accordingly  employ  it  with  great  success. 

You  know  that  Jupiter  has 
four  satellites  which  make  their 
revolutions  round  him,  each  in 
his  own  orbit,  as  represented 
in  the  annexed  figure,  Fig.  108, 
by  circles  described  round  Ju- 
piter. I  have  likewise  repre- 
sented the  sun  in  this  figure,  in 
order  to  exhibit  the  shadow 
A  O  B  behind  the  body  of  Ju- 
piter. You  see  the  first  of 
these  satellites,  marked  1,  on 
the  point  of  entering  into  the 
shadow ;  the  second,  marked  2, 
has  just  left  it ;  the  third,  3,  is 
still  at  a  great  distance,  but  ap- 
proaching to  it ;  and  the  fourth, 
4,  has  left  it  a  considerable 
time  ago. 

As  soon  as  one  of  these  satel- 
lites passes  into  the  shadow  it 
becomes  invisible,  and  that 
suddenly  ;  so  that  at  whatever 
place  of  the  globe  you  may  hap- 
pen to  be,  the  satellite  which 
was  before  distinctly  visible 
disappears  in  an  instant.  This 
entrance  of  a  satellite  into  the 
shadow  of  Jupiter  is  denomi- 
nated immersion,  and  its  depart- 
ure from  the  shadow  emer- 
sion ;  when  the  satellite  which 
had  for  some  time  been  invisible  suddenly  reappears. 

The  immersions  and  emersions  are  equally  adapted 
to  the  determination  of  the  longitude,  as  they  take 
place  at  a  decided  instant ;  so  that  when  such  a  phe- 
nomenon is  observed  at  several  places  of  the  globe, 


KNOWLEDGE    OF    THE    LONGITUDE.  177 

you  must  find  in  the  time  indicated  by  the  time- 
pieces of  each  the  difference  which  exactly  cor- 
responds to  the  difference  of  the  distance  of  their 
meridians.  It  is  the  same  thing  as  if  we  observed 
the  beginning  or  the  end  of  an  eclipse  of  the  moon ; 
and  the  case  is  then  involved  in  no  difficulty.  For 
some  time  past  we  have  been  able  to  calculate  these 
eclipses  of  the  satellites  of  Jupiter,  that  is,  their 
immersions  and  emersions ;  and  we  have  only  to 
compare  the  time  observed  with  the  time  calculated 
for  a  given  place,  say  Berlin,  in  order  to  conclude  at 
once  the  distance  of  its  meridian  from  that  of  our 
capital. 

This  method  is  accordingly  practised  universally 
in  travelling  by  land ;  but  the  means  have  not  yet 
been  discovered  of  profiting  by  it  at  sea,  where, 
however,  it  is  of  still  greater  importance  for  a  man 
to  know  with  certainty  where  he  is.-  Were  the 
satellites  of  Jupiter  as  visible  to  the  naked  eye  as 
the  moon  is,  this  method  would  be  attended  with  no 
difficulty,  even  at  sea ;  but  the  observation  cannot 
be  made  without  a  telescope  of  at  least  four  or  five 
feet  in  length — a  circumstance  which  presents  an  in- 
surmountable obstacle. 

You  well  know  that  it  requires  some  address  to 
manage,  even  on  land,  a  telescope  of  any  length,  to 
direct  it  towards  the  object  which  you  wish  to  con- 
template, and  to  keep  it  so  steady  as  not  to  lose  the 
object;  you  will  easily  comprehend,  then,  that  a 
ship  at  sea  being  in  a  continual  agitation,  it  must  be 
almost  impossible  to  catch  Jupiter  himself;  and  if 
you  could  find  him,  you  would  lose  him  again  in  a 
moment.  Now,  in  order  to  make  an  accurate  ob- 
servation of  the  immersion  or  emersion  of  one  of 
the  satellites  of  Jupiter,  it  is  absolutely  necessary 
that  you  should  have  it  in  your  power  to  look  at  him 
steadily  for  some  time  together ;  and  this  being  im- 
possible at  sea,  we  are  to  all  appearance  constrained 
to  abandon  this  method  of  determining  the  longitude. 


178  KNOWLEDGE    OF    THE    LONGITUDE. 

This  inconvenience,  however,  may  be  remedied 
two  ways ;  the  one  by  the  construction  of  telescopes 
six  inches  long,  or  less  still,  capable  of  discovering 
clearly  the  satellites  of  Jupiter ;  and  there  can  be  no 
doubt  that  these  would  be  more  manageable  than 
such  as  are  four  or  five  feet  in  length.  Artists  are 
actually  employing  themselves  with  success  in  bring- 
ing telescopes  of  this  sort  to  perfection ;  but  it  has 
not  yet  been  proved  whether  or  not  it  will  require  as 
much  address  to  point  them  to  tho  object  as  those 
which  are  longer. 

The  other  way  would  be  to  contrive  a  chair  to  be 
used  on  shipboard,  which  should  remain  fixed  and 
motionless,  so  as  not  to  be  affected  by  the  agitation 
of  the  vessel.  It  does  not  seem  impossible  that  a 
dexterous  mode  of  balancing  might  effect  this.  In 
fact,  it  is  not  long  since  we  read  in  the  public  prints 
that  an  Englishman  pretended  that  he  had  constructed 
such  a  chair,  and  therefore  claimed  the  prize  pro- 
posed for  the  discovery  of  the  longitude.*  His  claim 
was  well  founded,  if  he  indeed  constructed  the  ma- 
chine, as  it  would  be  possible  by  means  of  it  to  ob- 
serve at  sea  the  immersions  and  emersions  of  the 
satellites  of  Jupiter,  which  are  undoubtedly  very 
much  adapted  to  the  making  of  this  discovery ;  but 
for  some  time  past  no  further  mention  has  been  made 
of  it.  From  the  whole,  you  must  have  perceived 
how  many  difficulties  attach  themselves  to  the  dis- 
covery of  the  longitude. 

26th  September,  1761. 

*  The  invention  here  alluded  to  was  Irwin's  marine  chair,  -which 
was  tried  at  sea,  but  it  was  not  found  to  answer  the  purpose  of  the 
inventor. — Ed. 


KNOWLEDGE    OF    THE    LONGITUDE.  179 

LETTER  LII. 

The  Motion  of  the  Moon,  a  fifth  Method. 

THE  heavens  furnish  us  with  one  resource  more 
for  discovering  the  longitude  without  the  assistance 
of  telescopes,  in  which  astronomers  seem  to  place 
the  greatest  confidence.  It  is  the  moon,  not  only 
when  eclipsed  but  at  all  times,  provided  she  be  visi- 
ble;  an  unspeakable  advantage  considering  that 
eclipses  are  so  rare,  and  that  the  immersions  and 
emersions  of  the  satellites  of  Jupiter  are  of  such 
difficult  observation ;  there  being  a  considerable 
time  every  year  during  which  the  planet  Jupiter  is 
not  visible  to  us,  whereas  the  moon  is  almost  con- 
stantly in  view. 

You  must  undoubtedly  have  already  remarked, 
that  the  moon  rises  every  day  almost  three-quarters 
of  an  hour  later  than  the  preceding,  not  being  at- 
tached to  one  fixed  place  relatively  to  the  stars, 
which  always  preserve  the  same  situation  with  respect 
to  each  other,  though  they  have  the  appearance  of 
being  carried  round  by  the  heavens,  to  accomplish 
every  day  their  revolution  about  the  earth.  1  speak 
here  according  to  appearances ;  for  it  is  the  earth 
which  revolves  every  day  round  its  axis,  while  the 
heavens  and  the  fixed  stars  remain  at  rest ;  while 
the  sun  and  planets  are  continually  changing  their 
place  relatively  to  these.  The  moon  has  likewise  a 
motion  abundantly  rapid  from  one  day  to  another, 
with  relation  to  the  fixed  stars. 

If  you  were  to  see  the  moon  to-day  near  a  certain 
fixed  star,  it  will  appear  to-morrow  at  the  same 
hour  at  a  considerable  distance  from  it  towards  the 
east ;  and  the  distance  sometimes  exceeds  even  15 
degrees.  The  velocity  of  her  motion  is  not  always 
the  same,  yet  we  are  able  to  determine  it  very  ex- 


180  KNOWLEDGE    OF    THE    LONGITUDE. 

actly  for  every  day;  by  which  means  we  can  calcu- 
late before-hand  her  true  place  in  the  heavens  for 
every  hour  of  the  day,  and  for  any  known  meridian, 
say  that  of  Berlin,  or  Paris. 

Suppose,  then,  that  after  a  long  voyage  I  find  my- 
self at  sea,  in  a  place  altogether  unknown,  what  use 
can  I  make  of  the  moon,  in  order  to  discover  the 
longitude  of  the  place  where  I  am  ?  There  is  no 
difficulty  with  respect  to  the  latitude,  even  at  sea, 
where  there  are  means  abundantly  certain  for  ascer- 
taining the  height  of  the  pole,  to  which  the  latitude 
is  always  equal.  My  whole  attention,  then,  will  be 
directed  to  the  moon ;  1  will  compare  her  with  the 
fixed  stars  which  are  nearest,  and  thence  calculate 
her  true  place  relatively  to  them.  You  know  there 
are  celestial  globes  on  which  all  the  fixed  stars  are 
arranged,  and  that  celestial  charts  are  likewise  con- 
structed similar  to  geographical  maps,  on  which  are 
represented  the  fixed  stars  which  appear  in  a  certain 
quarter  of  the  heavens.  On  taking,  then,  a  celestial 
chart  on  which  the  fixed  stars  to  which  the  moon 
is  near  are  marked,  it  will  be  an  easy  matter  to  de- 
termine the  true  place  where  the  moon  at  that  time 
is ;  and  my  watch,  which  I  have  taken  care  to  regu- 
late there,  from  an  observation  of  the  moment  of 
noon,  will  indicate  to  me  the  time  of  my  lunar  ob- 
servation. Then,  from  my  knowledge  of  the  moon's 
motion,  I  calculate  for  Berlin,  at  what  hour  she  must 
appear  in  the  same  place  where  I  have  seen  her.  If 
the  time  observed  exactly  correspond  with  the  time 
of  Berlin,  it  will  be  a  demonstration  that  the  place 
where  I  am  is  precisely  under  the  meridian  of  Berlin, 
and  that  consequently  the  longitude  is  the  same. 
But  if  the  time  of  my  observation  is  not  that  of  Ber- 
lin, the  difference  will  give  that  which  is  between 
the  meridians  ;  and  reckoning  15  degrees  for  every 
hour  of  time,  I  compute  how  much  the  longitude  of 
the  place  I  am  at  is  greater  or  less  than  that  of  Ber- 


KNOWLEDGE    OF    THE    LONGITUDE.  181 

I'm:  the  place  where  time  is  more  advanced  has 
always  the  greater  longitude. 

This  is  an  abstract  of  the  manner  of  determining 
longitude  by  simple  observations  of  the  moon.  I 
remark,  that  the  happiest  moments  for  successfully 
performing  this  operation,  and  for  accurately  deter- 
mining the  moon's  place,  are,  when  a  fixed  star  hap- 
pens to  be  concealed  behind  her  body ;  this  is  called 
occupation,  and  there  are  two  instances  favourable 
to  observation,  that  when  the  moon  in  her  motion 
completely  covers  the  star,  and  that  when  the  star 
reappears.  Astronomers  are  particularly  attentive 
to  catch  these  instants  of  occupation,  in  order  to 
calculate  from  them  the  moon's  true  place. 

I  foresee,  however,  an  objection  you  will  proba- 
bly make  respecting  the  time-piece  with  which  I 
suppose  our  navigator  provided,  after  having  main- 
tained the  impossibility  of  constructing  one  that 
shall  be  proof  against  every  agitation  of  a  ship  at 
sea.  But  this  impossibility  respects  only  such 
time-pieces  as  are  expected  to  preserve  a  regular 
motion  for  a  long  time  together,  without  the  neces- 
sity of  frequent  adjustment ;  for  as  to  the  observa- 
tions in  question,  a  common  watch  is  quite  suffi- 
cient, provided  it  go  regularly  for  some  hours,  after 
having  been  carefully  adjusted  to  the  noon  of  the 
place  where  we  are;  supposing  a  doubt  to  arise, 
whether  we  could  calculate  from  it  the  succeeding 
evening  or  night,  at  the  time  we  observe  the  moon, 
the  stars  likewise  will  afford  the  means  of  a  new 
and  accurate  adjustment.  For  as  the  situation  of 
the  sun  with  relation  to  the  fixed  stars  is  perfectly 
known  for  any  time  whatever,  the  simple  observa- 
tion of  any  one  star  is  sufficient  to  determine  the 
place  where  the  sun  must  then  be ;  from  which  we 
are  enabled  to  calculate  the  hour  that  a  well  regu- 
lated timepiece  ought  to  indicate.  Thus,  at  the 
very  instant  of  making  an  observation  by  the  moon, 
we  are  enabled  likewise  to  regulate  our  timepiece 

VOL.  II.— Q 


182  KNOWLEDGE    OF    THE    LONGITUDE. 

by  the  stars ;  and  every  timepiece  is  supposed  to 
go  regularly  for  so  short  a  space. 
September,  1761. 


LETTER  LI1I. 

Advantages  of  this  last  Method ;  its  Degree  of 
Precision. 

THIS  last  method  of  finding  the  longitude,  founded 
on  lunar  observations,  seems  to  merit  the  prefer- 
ence, as  the  others  are  subjected  to  too  many  diffi- 
culties, or  the  opportunities  of  employing  them 
occur  too  seldom  to  be  useful.  And  you  must  be 
abundantly  sensible  that  success  depends  entirely 
on  the  degree  of  precision  attained  in  forming  the 
calculation,  and  that  the  errors  which  may  be  com- 
mitted would  lead  to  conclusions  on  which  we  could 
place  no  dependence.  It  is  of  importance,  there- 
fore, to  explain  what  degree  of  precision  we  may 
reasonably  hope  to  attain  in  reducing  this  method 
to  practice,  founded  on  the  considerable  change 
which  the  moon  undergoes  from  one  day  to  another 
in  her  position.  It  may  be  affirmed,  that  if  the 
moon's  motion  were  more  rapid,  it  would  be  more 
adapted  to  the  discovery  of  the  longitude,  and  would 
procure  for  us  a  higher  degree  of  precision.  But 
if,  on  the  contrary,  it  were  much  slower,  so  that 
we  could  scarcely  discern  any  change  of  her  posi- 
tion from  day  to  day,  we  could  derive  very  little, 
if  any,  assistance  from  her  towards  the  discovery 
of  the  longitude. 

Let  us  suppose,  then,  that  the  moon  changes  her 
place  among  the  fixed  stars  a  space  of  12  degrees 
in  twenty-four  hours  ;  she  will,  in  that  case,  change 
it  one  degree  in  two  hours,  and  half  a  degree,  or 
thirty  minutes  in  an  hour :  if  we  were  to  commit  a 
mistake  in  observing  the  moon's  place  of  thirty 


KNOWLEDGE    OF    THE    LONGITUDE.  183 

minutes,  it  would  be  the  same  thing  as  if  we  ob- 
served the  moon  an  hour  earlier  or  later,  and  we 
should  commit  a  mistake  of  one  hour  in  the  con- 
clusion respecting-  the  difference  of  the  meridians. 
Now,  one  hour's  difference  in  the  meridians  corres- 
ponds to  15  degrees  in  their  longitude;  conse- 
quently, we  should  be  mistaken  15  degrees  in  the 
longitude  itself  of  the  place  we  look  for;  which 
would  undoubtedly  be  an  error  so  enormous  that  it 
were  almost  as  well  to  know  nothing  about  it ;  and 
a  simple  computation  of  the  distance  and  the  direc- 
tion, however  uncertain,  could  not  possibly  lead  to  a 
mistake  so  very  gross.  But  a  man  must  have  gone 
to  work  in  a  very  slovenly  manner  to  commit  a 
mistake  of  30  minutes  respecting  the  moon's  place ; 
and  the  instruments  which  he  employed  must  have 
been  very  bad,  a  thing  not  to  be  supposed. 

Nevertheless,  however  excellent  the  instruments 
may  be,  and  whatever  degree  of  attention  may  have 
been  bestowed,  it  is  impossible  to  keep  clear  of  all 
error ;  and  he  must  have  acquitted  himself  very  well 
indeed  who  has  not  committed  the  mistake  of  one 
minute  in  determining  the  moon's  place.  Now,  as 
it  changes  half  a  degree,  or  30  minutes,  in  one  hour, 
it  will  change  one  minute  of  distance  in  two  minutes 
of  time.  When,  therefore,  the  mistake  of  the  moon's 
place  amounts  to  no  more  than  one  minute,  the 
mistake  in  the  difference  of  meridians  will  amount  to 
two  minutes  of  time.  And  one  hour,  or  60  minutes, 
being  equivalent  to  15  degrees  of  longitude,  there 
will  result  from  it  an  error  of  half  a  degree  in  the 
longitude ;  and  this  point  of  precision  might  be  suf- 
ficient for  every  purpose,  were  it  but  attainable. 

I  have  hitherto  supposed  our  knowledge  of  the 
moon's  motion  to  be  so  perfect,  that,  for  a  known 
meridian,  we  could  determine  the  moon's  true  place 
for  every  moment  without  an  error  ;  but  we  are  still 
very  far  short  of  that  point  of  perfection.  Within 
these  twenty  years,  the  error  in  this  calculation  was 


184  KNOWLEDGE    OF    THE    LONGITUDE. 

more  than  six  minutes ;  and  it  is  but  lately  that  the 
ingenious  Professor  Mayer  of  Gottingen,  pursuing 
the  track  I  had  pointed  out  to  him,  has  succeeded  so 
far  as  to  reduce  this  error  to  less  than  a  minute.  It 
may  very  easily  happen,  then,  that  in  the  calculation 
likewise,  the  error  of  one  minute  may  be  committed, 
which,  added  to  that  of  a  minute  committed  ih  the 
observation  of  the  moon's  place,  will  double  that 
which  results  from  it  respecting  the  longitude  of 
the  place  where  we. are;  and,  consequently,  it  may 
possibly  amount  to  a  whole  degree:  it  is  proper 
further  to  remark,  that  if  the  moon  in  twenty-four 
hours  should  change  her  relative  situation  more  than 
12  degrees,  the  error  in  the  longitude  would  be  less 
considerable.  The  means  may  perhaps  be  discov- 
ered of  diminishing  still  further  the  errors  into  which 
we  are  liable  to  fall,  in  the  observation  and  in  the 
calculation ;  and  then  we  should  be  able  to  ascertain 
the  longitude  to  a  degree,  or  less.  Nay,  we  ought 
not  to  despair  of  attaining  a  still  higher  degree  of 
precision.  We  have  only  to  make  several  observa- 
tions, which  can  be  easily  done  by  remaining  several 
days  together  at  the  same  place.  It  is  not  to  be 
apprehended,  in  that  case,  that  all  the  conclusions 
should  be  equally  defective ;  some  will  give  the  lon- 
gitude sought  too  great,  others  too  small,  and  by 
striking  a  medium  between  all  the  results,  we  may 
rest  assured  that  this  longitude  will  not  be  one  de- 
gree removed  from  the  truth. 

The  English  nation,  generously  disposed  to  engage 
genius  and  ability  in  this  important  research,  has 
proposed  three  prizes  for  ascertaining  the  longitude 
— one  of  10,000/.,  one  of  15,000/.,  and  one  of  20,0007. 
The  first  of  these  is  to  be  bestowed  on  the  person 
who  shall  determine  the  longitude  to  a  degree,  or 
about  it,  so  as  to  give  perfect  assurance  that  the 
error  shall  not  exceed  one  degree  at  most.  The 
second  is  to  be  given  to  him  who  shall  discover  a 
method  still  more  exact,  so  that  the  error  shall 


ON  THE  MARINER'S  COMPASS.  185 

never  exceed  two-thirds  of  a  degree,  or  40  minutes. 
The  highest  prize  is  destined  to  the  man  who  shall 
ascertain  the  longitude  so  exactly  that  the  error  shall 
never  exceed  half  a  degree,  or  30  minutes ;  and  a 
higher  degree  of  precision  is  hardly  to  be  expected. 
No  one  of  these  prizes  has  hitherto  been  allotted:  I 
do  not  take  into  the  account  the  gratification  be- 
stowed on  the  artist  who  pretended  to  it  from  his 
construction  of  perfect  timepieces.  Mr.  Mayer  is 
at  this  moment  claiming  the  highest,  and  I  think  he 
is  entitled  to  it.* 
3d  October,  1761. 


LETTER  LIV. 

On  the  Mariner's  Compass,  and  the  Properties  of  the 

Magnetic  Needle. 

You  are  by  this  time  sufficiently  informed  respect- 
ing the  discovery  of  the  longitude :  I  have  had  the 
pleasure  of  explaining  the  various  methods  which 
have  been  employed  for  the  determination  of  it. 

The  first  and  most  natural  is  carefully  to  observe 
the  quantity  of  space  which  we  have  gone  over,  and 
the  direction  in  which  we  moved ;  but  the  currents 
and  tempests  to  which  sea  voyages  are  exposed 
render  this  method  impracticable. 

The  second  requires  the  construction  of  a  time- 
piece so  perfect  as  to  go  always  uniformly,  notwith- 
standing the  agitation  of  a  ship  at  sea ;  which  no 
artist  has  hitherto  been  able  to  accomplish. 

The  third  is  founded  on  the  observation  of  the 
eclipses  of  the  moon,  which  would  completely 

*  The  widow  ofProfessor  Mayer  received  from  the  British  parliament 
a  reward  of  3000/.  sterling ;  and  Euler  himself  received  300Z.  for  furnish- 
ing the  theorems  on  which  Mayer's  Tables  are  founded.  The  latter  re- 
ceived also  a  reward  from  the  French  government,  and  gained  several 
prizes  for  his  improvement  of  the  lunar  theory. — Ed. 
Q  2 


186 

answer  every  purpose,  were  not  opportunities  of 
employing  it  too  rare,  and  least  in  our  power  when 
the  necessity  may  be  most  urgent. 

The  fourth  refers  to  the  eclipses  of  the  satellites 
of  Jupiter,  which  would  answer  the  purpose  ex- 
tremely well,  had  we  the  means  of  employing  at 
sea  telescopes  of  a  certain  description,  without 
which  they  are  invisible. 

Finally,  observations  of  the  moon  herself  furnish 
a  fifth  method,  which  appears  the  most  practicable, 
provided  we  were  able  to  observe  the  moon's  place 
in  the  heavens  so  exactly,  that  the  error  in  calcula- 
tion (and  error  is  unavoidable)  should  never  exceed 
one  minute,  in  order  to  be  assured  that  we  are  not 
mistaken  above  one  degree  in  the  determination  of 
the  longitude.*  » 

To.  one  or  the  other  of  these  five  methods  persons 
engaged  in  this  research  have  chiefly  directed  their 
speculations :  but  there  is  still  a  sixth,  which  seems 
likewise  adapted  to  the  solution  of  the  problem,  were 
it  more  carefully  cultivated ;  and  will  perhaps  one 
day  furnish  us  with  the  most  certain  method  of  dis- 
covering the  longitude ;  though  as  yet  we  are  far, 
very  far  short  of  it. 

It  is  not  derived  from  the  heavens,  but  is  attached 
to  the  earth  simply,  being  founded  on  the  nature  of 
the  magnet,  and  of  the  compass.  The  explication 
of  it  opens  to  me  a  new  field  of  important  physical 
observation,  for  your  amusement  and  instruction,  on 
the  subject  of  magnetism ;  and  I  flatter  myself  you 
will  attend  with  delight  and  improvement  to  the 
elucidations  which  I  am  going  to  suggest. 

My  reflections  shall  be  directed  only  to  the  main 
subject  of  our  present  research,  I  mean  the  discovery 
of  the  longitude.  I  remark  in  general,  that  the 

*  This  method  is  now  brought  to  very  great  perfection,  not  only  by 
the  improvement  of  the  lunar  tables,  but  by  the  perfection  of  the 
sextants  and  circles  with  which  the  moon's  place  in  the  heavens  is 
observed.— Ed. 


ON  TIIK  MARINER'S  COMPASS.  187 

magnet  is  a  stone  which  has  the  quality  of  attracting 
iron,  and  of  disposing  itself  in  a  certain  direction ; 
and  that  it  communicates  the  same  quality  to  iron 
and  steel,  by  rubbing,  or  simply  touching  them  with 
a  magnet ;  proposing  afterward  to  enter  into  a  more 
minute  discussion  of  this  quality,  and  to  explain  the 
nature  of  it. 

1  begin,  then,  with  the  description  of  a  magnetic 
needle,  which,  mounted  in  a  certain  manner,  for  the 
use  of  .mariners,  is  denominated  the  compass. 

For  this  purpose  we  provide  a  needle  of  good 
steel,  nearly  resembling  Fig.  109,  one  extremity  of 
Fig.  109. 


which  B  terminates  in  a  point,  the  better  to  distin- 
guish it  from  the  other  A;  it  is  furnished  at  the 
middle  C  with  a  small  cap,  hollowed  below,  for  the 
purpose  of  placing  the  needle  on  a  pivot  or  point  D, 
as  may  be  seen  in  the  second  figure. 

The  two  ends  are  adjusted  in  such  a  manner,  that 
the  needle,  being  in  perfect  equilibrium,  can  revolve 
freely,  or  remain  at  rest,  on  the  pivot,  in  whatever 
situation  it  may  be  placed.  Before  the  magnet  is 
applied,  it  would  be  proper  to  temper  the  needle,  in 
order  to  render  it  as  hard  as  possible  ;  then  by  rub- 
bing or  touching  it  with  a  good  loadstone,  it  will 
instantly  acquire  the  magnetic  virtue.  The  two  ex- 
tremities will  no  longer  balance  each  other,  but  the 
one  B  will  descend,  as  if  it  had  become  heavier; 
and  in  order  to  restore  the  equilibrium,  something 
must  be  taken  away  from  the  extremity  B,  or  a  small 
weight  added  to  the  end  A.  But  the  artists,  fore- 
seeing this  change  produced  by  magnetism,  make 
the  end  B  originally  lighter  than  the  end  A,  that  the 


188  ON  THE  MARINER'S  COMPASS. 

magnetized  needle  may  of  itself  assume  the  hori- 
zontal position. 

It  then  acquires  another  property  still  more  re- 
markable :  it  is  no  longer  indifferent  to  all  situations 
as  formerly ;  but  affects  one  in  preference  to  every 
other,  and  disposes  itself  in  such  a  manner  that  the 
extremity  B  is  directed  to  the  north  nearly,  and  the 
extremity  A  towards  the  south ;  and  the  direction 
of  the  magnetic  needle  corresponds  almost  with  the 
meridian  line. 

You  recollect  that,  in  order  to  trace  a  meridian 
line,  which  may  point  out  the  north  and  the  south, 
it  is  necessary  to  have  recourse  to  astronomical 
observations,  as  the  motion  of  the  sun  and  stars 
determines  that  direction;  and  when  we  are  not 
provided  with  the  necessary  instruments,  and  espe- 
cially when  the  sky  is  overclouded,  it  is  impossible 
to  derive  any  assistance  from  the  heavens  towards 
tracing  the  meridian  line ;  this  property  of  the  mag- 
netic needle  is,  therefore,  so  much  the  more  admi- 
rable, that  it  points  out,  at  all  times,  and  in  every 
place,  the  northern  direction,  on  which  depends  the 
others,  towards  the  east,  south,  and  west.  For  this 
reason  the  use  of  the  magnetic  needle,  or  compass, 
is  become  universal. 

It  is  in  navigation  that  the  advantages  resulting 
from  the  use  of  the  compass  are  most  conspicuous ; 
it  being  always  necessary  to  direct  the  course  of  a 
vessel  towards  a  certain  quarter  of  the  world,  in 
order  to  reach  a  place  proposed,  conformably  to 
geographic  or  marine  charts,  which  indicate  the 
direction  in  which  we  ought  to  proceed.  Before  this 
discovery,  accordingly,  it  was  impossible  to  under- 
take long  voyages ;  the  mariner  durst  not  lose  sight 
of  the  coast  for  fear  of  mistaking  his  course,  unless 
the  sky  was  unclouded,  and  the  stars  pointed  out 
the  way. 

A  vessel  on  the  wide  ocean,  without  the  know- 
ledge of  the  proper  course,  would  be  precisely  in  the 


ON  THE  MARINER'S  COMPASS.  189 

state  of  a  man  who,  with  a  bandage  over  his  eyes, 
was  obliged  to  find  his  way  to  the  great  church  of 
Magdeburg ;  imagining  he  was  going  one  way,  he 
might  be  going  another.  The  compass,  then,  is  the 
principal  guide  in  navigation ;  and  it  was  not  till 
after  this  important  discovery  that  men  ventured 
across  the  ocean,  and  attempted  the  discovery  of 
a  new  world.  What  would  a  pilot  do  without  his 
compass  during  or  after  a  storm,  when  he  could 
derive  no  assistance  from  the  heavens  1  Take 
whatever  course  he  might,  he  must  be  ignorant  in 
what  direction  he  was  proceeding,  north,  south,  or 
to  any  other  quarter.  He  would  presently  deviate 
to  such  a  degree  as  infallibly  to  lose  himself.  But 
the  compass  immediately  puts  him  right ;  from 
which  you  will  be  enabled  to  judge  of  the  importance 
of  the  discovery  of  the  magnetic  needle,  or  mariner's 
compass. 

6th  October,  1761. 


LETTER  LV. 

Declination  of  the  Compass,  and  Manner  of  observing  it. 

THOUGH  the  magnetic  needle  affects  the  situation 
of  being  directed  from  south  to  north,  there  are  ac- 
cidental causes  capable  of  deranging  this  direction, 
which  must  be  carefully  avoided.  Such  are  the 
proximity  of  a  loadstone,  or  of  iron  or  steel.  You 
have  only  to  present  a  knife  to  a  magnetic  needle, 
and  it  will  immediately  quit  its  natural  direction,  and 
move  towards  the  knife  ;  and,  by  drawing  the  knife 
round  the  needle,  you  will  make  it  assume  every 
possible  direction.  In  order  to  be  assured,  then, 
that  the  needle  is  in  its  natural  direction,  you  must 
keep  at  a  distance  from  it  all  iron  or  steel,  as  well 
as  magnets  ;  which  is  so  much  the  more  easy,  that 
these  substances  influence  its  direction  only  when 


190 


ON  THE  MARINER'S  COMPASS. 


very  near  it :  once  removed,  their  effect  becomes  in- 
sensible, unless  in  the  case  of  a  very  powerful  mag- 
net, which  might  possibly  act  on  the  needle  at  the 
distance  of  several  feet. 

But  iron  alone  produces  not  this  effect,  as  the 
compass  may  be  used  to  advantage  even  in  iron 
mines.  You  are  perfectly  sensible,  that  under 
ground,  in  mines,  we  are  in  the  same  condition  as  at 
sea  when  the  face  of  heaven  is  overclouded,  and  that 
it  is  necessary  to  drive  mines  in  a  certain  direction. 
Plans  are  accordingly  constructed  representing  all 
the  tracks  hollowed  out  in  the  bowels  of  the  earth, 
and  this  operation  is  regulated  merely  by  the  com- 
pass ;  this  is  the  object  of  the  science  denominated 
subterraneous  geometry. 

To  return  to  our  compass  or  magnetic  needle: 
I  have  remarked  that  its  direction  is  only  almost 
northerly ;  it  is  therefore  incorrect  to  say  that  the 
magnet  has  the  property  of  always  pointing  north. 
Having  employed  myself  in  the  fabrication  of  many 
magnetic  needles,  I  constantly  found  that  their  di- 
rection at  Berlin  deviated  about  15°  from  the  true 
meridian  line ;  now  an  aberration  of  15°  is  very  con- 
siderable. 

Fig.  110  represents  first  the 
true  meridian  line,  drawn  from 
north  to  south ;  that  which  is 
drawn  at  right  angles  with  it 
'ndicates  the  east  to  the  right- 
hand,  and  the  west  to  the  left. 
Now  the  magnetic  needle  A  B 
does  not  fall  on  the  meridian, 
but  deviates  from  it  an  angle 
of  15°  B  0  North.  This  angle  is 
denominated  the  declination, 
and  sometimes  the  deviation  or 
variation,  of  the  compass  or  magnetic  needle  ;  and 
as  the  extremity  B,  nearest  the  north,  deviates 


ON  THE  MARINERS  COMPASS.        191 

towards  the  west,  we  say  the  declination  is  15° 
westerly. 

Having  thus  determined  the  declination  of  the 
magnetic  needle,  we  can  make  it  answer  the  same 
purpose  as  if  it  pointed  directly  north.  The  needle 
is  usually  enclosed  in  a  circle,  and  you  have  only  to 
mark  on  it  the  due  north  and  the  exact  distance  from 
the  northern  extremity  of  the  needle,  so  as  to  make 
a  declination  of  15°  westward  ;  and  the  line  North 
South,  Fig.  110,  will  indicate  the  true  meridian  line, 
and  enable  us  to  ascertain  the  four  cardinal  points, 
north,  east,  south,  and  west. 

The  better  to  disguise  the  secret,  the  magnetic 
needle  is  concealed  in  a  circle  of  pasteboard,  as  rep- 
resented in  the  figure,  only  the  needle  is  rendered 
invisible,  the  pasteboard  covering  it,  and  forming 
but  one  body  with  it,  the  centre  of  which  is  placed 
on  a  pivot,*  in  order  to  admit  of  a  free  revolution : 
it  assumes,  of  course,  a  situation  such  that  the  point 
marked  North  is  always  directed  to  that  point  of  the 
horizon  ;  whereas  the  needle,  which  is  not  seen,  in 
effect  deviates  from  it  15°  to  the  west.  This  con- 
struction serves  only  to  disguise  th'e  declination, 
which  the  vulgar  consider  as  a  defect,  though  it  be 
rather  an  object  worthy  of  admiration,  as  we  shall 
afterward  see ;  and  the  pasteboard,  only  increasing 
the  weight  of  the  needle,  prevents  its  turning  so 
freely  as  if  it  were  unencumbered. 

To  remedy  this,  and  more  commodiously  to 
•employ  the  compass,  the  needle  is  deposited  in  a 
circular  box,  the  circumference  of  which,  divided 
into  360°,  exhibits  the  names  of  the  principal 
points  of  the  horizon.  In  the  centre  is  the  pivot, 
or  point  which  supports  the  needle,  and  this  last 
immediately  assumes  a  certain  direction ;  the  box  is 
then  turned  till  the  northern  extremity  of  the  needle 

*  The  cap  or  hollow  which  rests  on  the  pivot  should  be  made  of  gar- 
net, which  gives  less  friction  than  any  other  of  the  precious  stones.— Ed. 


192 

B  exactly  corresponds  with  15°  on  the  circumference, 
reckoning  from  the  north-westward  ;  and  then  the 
names  marked  will  agree  with  the  real  quarters  of 
the  world. 

At  sea,  however,  they  employ  needles  cased  in 
circles  of  pasteboard,  the  circumference  of  which  is 
divided  into  360°,  to  prevent  the  necessity  of  turning 
round  the  box ;  then  the  pasteboard  circle,  which  is 
called  the  compass,  indicating  the  real  quarters  of 
the  world,  we  have  only  to  refer  to  it  the  course 
which  the  ship  is  steering,  in  order  to  ascertain  the 
direction,  whether  north  or  south,  east  or  west,  or 
any  other  intermediate  point.  By  the  compass  like- 
wise we  distinguish  the  winds,  or  the  quarters  from 
which  they  blow ;  and  from  the  points  marked  on  it 
their  names  are  derived.  It  is  necessary,  at  any 
rate,  to  be  perfectly  assured  of  the  declination  or 
variation  of  the  compass ;  we  have  found  it  to  be 
exactly  15°  westward  here  at  Berlin ;  but  it  may  be 
different  at  other  places,  as  I  shall  afterward  demon- 
strate. 

10th  October,  1761. 


LETTER  LVI. 

Difference   in  the  Declination  of  the  Compass  at   the 
same  Place. 

WHEN  I  say  that  the  declination  of  the  compass 
is  15°  west,  this  is  to  be  understood  as  applying  only 
to  Berlin,  and  the  present  time  :  for  it  has  been  re- 
marked, that  not  only  is  this  declination  different  at 
different  places  of  the  earth,  but  that  it  varies,  with 
time,  at  the  same  place.* 

The  magnetic  declination  is  accordingly  much 

*  In  the  year  1786,  M.  Schulze  found  the  deviation  to  be  18°  28'  which 
seems  to  have  been  its  maximum.  In  1805,  M.  Bode  found  it  to  be  18°  3', 
having  been  so  low  as  17°  5'  in  1788.  -Ed. 


ON  THE  MARINER'S  COMPASS.  193 

greater  at  Berlin  now  than  it  was  formerly.  I  re- 
collect the  time  perfectly  when  it  was  only  10°;* 
and  in  the  last  century  there  was  a  period  when 
there  was  no  declination,  so  that  the  direction  of  the 
magnetic  needle  coincided  exactly  with  the  meridian 
line.  This  was  about  the  year  1670 ;  since  then  the 
declination  is  become  progressively  greater  towards 
the  west,  up  to  15°,  as  at  this  day :  and  there  is  every 
appearance  that  it  will  go  on  diminishing  till  it  is 
again  reduced  to  nothing.  I  give  this,  however, 
merely  as  conjecture,  for  we  are  very  far  from  being 
able  to  predict  it  with  certainty. 

Besides,  it  is  well  known  that  prior  to  the  year 
1670,  the  declination  was  in  the  contrary  direction, 
that  is,  towards  the  east ;  and  the  farther  back  we 
go,  the  greater  do  we  find  the  declination  eastward. 
Now,  it  is  impossible  to  go  farther  back  than  to  the 
period  when  the  compass  was  discovered ;  this  hap- 
pened in  the  fourteenth  century  ;  but  it  was  long 
after  the  discovery  before  they  began  to  observe 
the  declination  at  Berlin ;  for  it  was  not  perceived 
at  first  that  the  needle  deviated  from  the  meridian 
line. 

But  at  London,  where  this  subject  has  been  more 
carefully  studied,  the  magnetic  declination  in  the 
year  1580  was  observed  to  be  11°  15'  east;  in  1622, 
6°  0'  east ;  in  1634,  4°  5'  east ;  in  1657  there  was  no 
declination;  but  in  1672  it  was  2°  30'  west;  in 
1692,  6°  0'  west ;  and  at  present  it  may  probably  be 
18°  west,  or  more.f  You  see,  then,  that  about 
the  beginning  of  the  last  century,  the  declination 
was  nearly  8  degrees  east :  that  thenceforward  it , 
gradually  diminished,  till  it  became  imperceptible  in 
the  year  1657 ;  and  that  it  has  since  become  westerly, 
gradually  increasing  up  to  the  present  time.J 

*  It  was  so  low  as  10°  at  Berlin  in  1717. — Ed. 

t  In  January,  1821,  the  variation  of  the  needle  at  London  was  24°  35 
west.— Ed. 

t  The  variation  of  the  magnet  is  not  only  different  in  different  coun- 
tries, but  in  different  places  in  the  same  country,  situated  a  few  miles 

VOL.  II.— R 


194  ON  THE  MARINER'S  COMPASS. 

It  has  preserved  nearly  the  same  order  at  Paris ; 
but  there  it  was  reduced  to  nothing  in  1666,  nine 
years  later  than  at  London ;  hence  you  will  observe 
a  most  unaccountable  diversity  of  declination  rela- 
tively to  different  places  of  the  earth  at  the  same 
time,  and  to  the  same  place  at  different  times. 

At  present,  not  only  through  all  Europe,  but 
through  all  Africa,  and  the  greatest  part  of  Asia,  the 
declination  is  westerly,  in  some  places  greater,  in 
others  less,  than  with  us.  It  is  greater  in  certain 
countries  of  Europe  than  at  our  capital :  namely,  in 
Scotland  and  in  Norway,  where  the  declination  con- 
siderably exceeds  20°  ;  in  Spain,  Italy,  and  Greece, 
on  the  contrary,  it  is  less,  being  about  12°  ;  on  the 
western  coasts  of  Africa  it  is  about  10°,  and  on  the 
eastern  12°.  But  as  you  advance  eastward  into 
Asia  it  progressively  diminishes,  till  it  entirely  dis- 
appears in  the  heart  of  Siberia,  at  Jeniseisk  ;  it  dis- 
appears too  in  China,  at  Pekin,  and  at  Japan ;  but 
beyond  these  regions,  to  the  eastward,  the  declina- 
tion becomes  easterly,  and  goes  on  increasing  in 
this  direction,  along  the  north  part  of  the  Pacific 
Ocean,  to  the  western  coasts  of  America,  from 
which  it  proceeds,  gradually  diminishing,  till  it 
again  disappears  in  Canada,  Florida,  the  Antilles, 
and  towards  the  coasts  of  Brazil.  Beyond  these 
countries,  towards  the  east,  that  is,  towards  Europe 
and  Africa,  it  again  becomes  westerly,  as  I  have 
already  remarked. 

In  order  to  attain  a  perfect  knowledge  of  the  pres- 
ent state  of  magnetic  declination,  it  would  be  neces- 
sary to  ascertain  for  all  places,  both  at  land  and  sea, 
the  present  state  of  magnetic  declination,  and  whether 

from  each  other.  It  is  also  subject  to  an  hourly  "change  or  movement  at 
the  same  place  on  the  same  day,  returning  generally  to  the  same  point, 
very  nearly,  at  the  same  hour  on  each  successive  day.  In  the  year  1820 
agreeably  to  Professor  Fisher,  the  variation  at  New-Haven  was  4°  25'  25" 
VV.  The  annual  variation  is  2'  49" :  so  that  the  needle  appears  to  be  grad- 
ually advancing  towards  the  true  meridian,  after  which  it  will  probably 
acquire  an  easterly  variation.— Am.  Ed. 


ON  THE  MARINER'S  COMPASS.  195 

its  tendency  is  westward  or  eastward.  This  know- 
ledge would  be  undoubtedly  extremely  useful,  but 
we  dare  scarcely  hope  for  it.  It  would  require  men 
of  ability  in  every  part  of  the  globe, -employed  at  the 
same  time  in  observing,  each  on  his  own  station,  the 
magnetic  declination,  and  who  should  communicate 
their  observations  with  the  utmost  exactness.  But 
the  space  of  some  years  would  elapse  before  the 
communications  of  the  more  remote  could  be  re- 
ceived,4hus  the  knowledge  aimed  at  is  unattainable 
till  after  the  expiration  of  years.  Now,  though  no 
very  considerable  change  takes  place  in  the  direc- 
tion of  the  magnetic  needle  in  two  or  three  years, 
this  change,  however  'small,  would  prevent  the 
attainment  of  complete  information  respecting  the 
present  state  of  the  various  declination  of  the  mag- 
netic needle,  from  observations  made  at  the  same 
time  in  the  different  regions  of  the  globe. 

The  same  thing  holds  with  respect  to  times  past ; 
to  every  year  corresponds  a  certain  state  of  mag- 
netic declination  proper  to  itself,  and  which  distin- 
guishes it  from  every  other  period  of  time,  past  and 
future.  It  were,  however,  sincerely  to  be  wished 
that  we  had  an  exactly  detailed  state  of  the  declina- 
tion for  one  year  only;  the  most  important  elu- 
cidations of  the  subject  would  certainly  be  derived 
from  it. 

The  late  Mr.  Halley,  a  celebrated  English  astrono- 
mer, has  attempted  to  do  this  for  the  year  1700, 
founding  his  conclusions  on  a  great  number  of  ob- 
servations made  at  different  places,  both  by  land  and 
sea ;  but,  besides  that  some  very  considerable  dis- 
tricts, where  these  observations  were  not  made,  are 
not  taken  into  his  account,  most  of  those  which 
he  has  employed  were  made  several  years  prior  to 
1700 ;  so  that  at  this  era  the  declination  might  have 
undergone  very  considerable  alterations.  It  follows 
that  this  statement,  which  we  find  represented  on  c 
general  chart  of  the  earth,  must  be  considered  as  ex  • 


198  ON  THE  MARINER'S  COMPASS. 

tremely  defective ;  and,  moreover,  what  would  it  now 
avail  us  to  know  the  state  of  magnetic  declination 
for  the  year  1700,  having  since  that  time  undergone 
a  considerable  change  ? 

Other  English  geographers  have  produced,  pos- 
terior to  that  period,  a  similar  chart,  intended  to 
represent  all  the  declinations  such  as  they  were  in 
the  year  1744.  But  as  it  has  the  same  defect  with 
that  of  Mr.  Halley,  and  as  they  likewise  were  unable 
to  procure  observations  from  several  countries  on 
the  globe,  they  did  not  scruple  to  fill  up  the  vacant 
places  by  consulting  Halley's  chart,  which  certainly 
could  not  apply  to  1744.  You  will  conclude,  from 
what  I  have  said,  that  our  knowledge  of  this  im- 
portant branch  of  physics  is  extremely  imperfect.* 

13th  October,  1761. 


LETTER  LVII. 

Chart  of  Declinations ;  Method  of  employing  it  for  the 
Discovery  of  the  Longitude. 

IT  may  be  proper  likewise  to  explain  in  what 
manner  Halley  proceeded  to  represent  the  magnetic 
declinations  in  the  chart  which  he  constructed  for 
the  year  1700,  that  if  you  should  happen  to  see  it, 
you  may  comprehend  its  structure. 

First,  he  marked  at  every  place  the  declination  of 
the  magnetic  needle,  such  as  it  had  been  there  ob- 
served. He  distinguished,  among  all  these  places, 
those  where  there  was  no  declination,  and  found 
that  they  all  fall  in  a  certain  line,  which  he  calls  the 
line  of  no  declination,  as  everywhere  under  that  line 

*  Very  correct  and  interesting  charts,  both  of  the  variation  and  the  dip  of 
the  magnetic  needle,  have  been  recently  constructed  by  Mr.  Hansteen  of 
Christiania  in  Norway,  and  published  in  his  very  able  work  on  the  Mag- 
netism of  the  Earth.  Mr.  Hansteen 's  charts  will  be  found  in  the  Edin- 
burgh Philosophical  Journal,  vol.  iv.  p.  363.— Ed. 


ON  THE  MARINER'S  COMPASS.  197 

there  was  then  none.  This  line  was  neither  a  me- 
ridian nor  a  parallel,  but  ran  in  a  very  oblique  direc- 
tion over  North  America,  and  left  it  near  the  coasts 
of  Carolina;  thence  it  bent  its  course  across  the 
Atlantic  Ocean,  between  Africa  and  America.  Be- 
sides this  line,  he  discovered  likewise  another  in 
which  the  declination ,  disappeared ;  it  descended 
through  the  middle  of  China,  and  passed  from  thence 
through  the  Philippine  Isles  and  New-Holland.  It 
is  easy  to  judge,  from  the  track  of  these  two  lines, 
that  they  have  a  communication  near  both  poles  of 
the  globe. 

Having  fixed  these '  two  lines  of  no  declination, 
Mr.  Halley  remarked  that  everywhere  between  the 
first  and  last,  proceeding  from  west  to  east,  that  is, 
through  all  Europe,  Africa,  arid  almost  the  whole  of 
Asia,  the  declination  was  westerly ;  and  that  on  the 
other  side,  between  those  lines,  that  is,  over  the 
whole  Pacific  Ocean,  it  was  easterly.  After  this, 
he  observed  all  the  places  in  which  the  declination 
was  5  degrees  west,  and  found  he  could  still  con- 
veniently draw  a  line  through  all  these  places,  which 
he  calls  the  line  of  five  degrees  west.  He  found  like- 
wise two  lines  of  this  description,  the  one  of  which 
accompanied,  as  it  were,  the  first  of  no  declination, 
and  the  other  the  last.  He  went  on  in  the  same 
manner  with  the  places  where  the  declination  was 
10°  ;  afterward  15°,  20°,  &c. ;  and  he  saw  that  these 
lines  of  great  declination  were  confined  to  the  polar 
regions ;  whereas  those  of  small  declination  encom- 
passed the  whole  globe,  and  passed  through  the 
equator. 

In  fact,  the  declination  scarcely  ever  exceeds  15° 
on  the  equator,  whether  west  or  east;  but  on  ap- 
proaching the  poles,  it  is  possible  to  arrive  at  places 
where  the  declination  exceeds  58°  and  60°.  There 
are  undoubtedly  some  where  it  is  still  greater,  ex- 
ceeding even  90°,  and  where  the  northern  extremity 
R2 


198          ON  THE  MARINER'S  COMPASS. 

of  the  needle  will  consequently  turn  about  and  point 
southward.* 

Finally,  having  drawn  similar  lines  through  the 
places  where  the  declination  was  eastward  10°,  15°, 
20°,  and  so  on,  Mr.  Halley  filled  up  the  whole  chart, 
which  represented  the  entire  surface  of  the  earth, 
under  each  of  which  lines  the  declination  is  univer- 
sally the  same,  provided  the  observations  are  not 
erroneous.  Mr.  Halley  has  accordingly  scrupulously 
abstained  from  continuing  such  lines  beyond  the 
places  where  observations  had  actually  been  made : 
for  this  reason  the  greater  part  of  his  chart  is  a 
blank. 

Had  we  such  a  chart  accurate  and  complete,  we 
should  see  at  a  glance  what  declination  must  have 
predominated  at  each  place  at  the  time  for  which 
the  chart  was  constructed  ;  and  though  the  place  in 
question  should  not  be  found  precisely  under  one 
of  the  lines  traced  on  the  chart,  by  comparing  it 
with  the  two  lines  between  which  it  might  be  situ- 
ated, 0we  could  easily  calculate  the  intermediate 
declination  which  corresponds  to  it.  If  I  found  my 
present  place  to  be  between  the  lines  of  10°  and  15° 
of  western  declination,  I  should  be  certain  that  the 
declination  there  was  more  than  10°,  and  less  than 
15°  ;  and  according  as  I  might  be  nearer  the  one  or 
the  other,  I  could  easily  find  the  means  which  would 
indicate  the  true  declination. 

From  this  you  will  readily  comprehend,  that  if  we 
had  such  a  chart  thus  exact,  it  would  assist  us  in 
discovering  the  longitude,  at  least  for  the  time  to 
which  it  corresponded.  In  order  to  explain  this 
method,  let  us  suppose  that  we  are  possessed  of  a 
chart  constructed  for  the  present  year,  we  would  see 
on  it,  first,  the  two  lines  drawn  through  the  places 

*  This  was  found  to  be  the  case  in  the  voyages  of  Captain  Ross  and 
Captain  Parry.  On  the  S.E.  point  of  Byam  Martin's  Island,  in  west 
Ion.  103°  44£',  and  north  lat.  75°  9',  the  variation  was  1R5°  50'  east, 
having  been  128°  50' west  in  west  Ion.  91°  47',  and  north  !at.  74°  40'.— Ed. 


ON  THE  MARINER'S  COMPASS.  199 

where  there  is  no  declination ;  then  the  two  where 
it  is  5°,  10°,  15°,  20°,  both  east  and  west :  let  us  fur- 
ther suppose  that,  for  the  greater  exactness,  these 
lines  were  drawn  from  degree  to  degree,  and  that  I 
found  myself  at  a  certain  place  on  sea,  or  in  an  un- 
known country,  I  would  in  the  first  place  draw  a  me- 
ridian line,  in  order  to  ascertain  how  much  my  com- 
pass deviated  from  it,  and  I  should  find,  for  example, 
that  the  declination  is  precisely  10°  east ;  I  should 
then  take  my  chart,  and  look  for  the  two  lines  under 
which  the  declination  is  10°  east,  fully  assured  that 
I  am  under  the  one  or  the  other  of  these  two  lines, 
which  must  at  once  greatly  relieve  my  uncertainty. 
Finally,  I  would  observe  the  height  qf  the  pole, 
which  being  the  latitude  of  my  place,  nothing  more 
would  remain  but  to  mark,  on  the  two  lines  men- 
tioned, the  points  where  the  latitude  is  the  same 
with  that  which  I  have  .just  observed,  and  then  all 
my  uncertainty  is  reduced  to  two  points  very  dis- 
tant from  each  other ;  now  the  circumstances  of  my 
voyage  would  easily  determine  which  of  those  two 
places  is  that  where  I  actually  am. 

You  will  admit  that  if  we  had  charts  such  as  I 
have  described,  this  method  would  be  the  most  com- 
modious and  accurate  of  all  for  ascertaining  the 
longitude  ;  but  this  is  precisely  the  thing  we  want ; 
and  as  we  are  still  very  far  from  having  it  in  our 
power  to  construct  one  for  the  time  past,  which 
would  be  of  no  use  for  the  present  time,  for  want  of 
a  sufficient  number  of  observations,  we  are  still  less 
instructed  respecting  all  the  changes  of  declination 
which  every  place  undergoes  in  the  lapse  of  time. 
The  observations  hitherto  made  assure  us  that  cer- 
tain places  are  subject  to  very  considerable  varia- 
tions, and  that  others  scarcely  undergo  any,  in  the 
same  interval  of  time ;  which  strips  us  of  all  hope 
of  ever  being  able  to  profit  by  this  method,  however 
excellent  it  may  be  in  itself. 

llth  October,  1761. 


200       ON  THE  MAGNETIC  NEEDLE. 


LETTER  LVIII. 

Why  does  the  Magnetic  Needle  affect,  in  every  Place  of 
the  Earth,  a  certain  Direction,  differing  in  different 
Places ;  and  for  what  Reason  does  it  change,  with 
Time,  at  the  same  Place  ? 

You  will  undoubtedly  have  the  curiosity  to  be  in- 
formed why  magnetic  needles  affect,  at  every  place 
on  the  globe,  a  certain  direction ;  why  this  direction 
is  not  the  same  at  different  places ;  and  why,  at  the 
same  place,  it  changes  with  the  course  of  time.  I 
shall  answer  these  important  inquiries  to  the  best 
of  my  ability,  though,  I  fear,  not  so  much  to  your 
satisfaction  as  I  could  wish. 

I  remark,  first,  that  magnetic  needles  have  this 
property  in  common  with  all  magnets,  and  that  it  is 
only  their  form,  and  their  being  made  to  balance  and 
revolve  freely  on  a  pivot,  which  renders  it  more  con- 
spicuous. The  loadstone,  suspended  by  a  thread, 
turns  towards  a  certain  quarter,  and  when  put  in  a 
small  vessel  to  make  it  swim  on  water,  the  vessel 
which  supports  the  loadstone  will  always  affect  a 
certain  direction.  Every  loadstone  fitted  with  two 
opposite  points,  the  one  of  which  is  directed  to  the 
north,  and  the  other  to  the  south,  will  be  subject  to 
the  same  variations  as  the  magnetic  needle. 

These  points  are  very  remarkable  in  all  load- 
stones, as  by  them  iron  is  attracted  with  the  greatest 
force. 

They  are  denominated  the  poles  of  a  loadstone — a 
term  borrowed  from  that  of  the  poles  of  the  earth, 
or  of  the  heavens  ;  because  the  one  has  a  tendency 
towards  the  north,  and  the  other  towards  the  south 
pole  of  the  earth :  but  this  is  to  be  understood  as 
only  almost,  not  exactly,  the  case ;  for  when  the 


ON  THE  MAGNETIC  NEEDLE.       201 

name  was  imposed,  the  declination  had  not  yet  been 
observed.  That  pole  of  the  loadstone  which  is  di- 
rected northward  is  called  its  north  pole,  and  that 
which  points  southward  its  south  pole. 

I  have  already  remarked,  that  a  magnetic  needle, 
as  well  as  the  loadstone  itself,  assumes  this  situation, 
which  appears  natural  to  it  only  when  removed 
from  the  vicinity  of  another  loadstone,  or  of  iron. 
When  a  magnetic  needle  is  placed  near  a  loadstone, 
its  situation  is  regulated  by  the  poles  of  that  load- 
stone :  so  that  the  north  pole  of  the  loadstone  attracts 
the  southern  extremity  of  the  needle ;  and  recipro- 
cally, the  south  pole  of  the  loadstone  the  northern 
extremity  of  the  needle.  For  this  reason,  in  refer- 
ring one  loadstone  to  another,  we  call  those  the 
friendly  poles  which  bear  different  names,  and  those 
the  hostile  which  have  the  same  name.  This  prop- 
erty is  singularly  remarkable  on  bringing  two  load- 
stones near  each  other ;  for  then  we  find,  that  not 
only  do  the  poles  of  different  names  mutually  attract, 
but  that  those  of  the  same  name  shun  and  repel  each 
other.  This  is  still  more  conspicuous  when  two 
magnetic  needles  are  brought  within  the  sphere  of 
mutual  influence. 

In  order  to  be  sensible  of  this,  it  is  of  much  im- 
portance to  consider  the  situation  which  a  magnetic 
needle  assumes  in  the  vicinity  of  a  loadstone. 

The  bar  AB,  Fig.  Ill,  represents  a  loadstone, 

Fig.  111. 


202  ON    THE    MAGNETIC    NEEDLE. 

whose  north  pole  is  B,  and  the  south  pole  A :  you 
see  various  positions  of  the  magnetic  needle,  under 
the  figure  of  an  arrow,  whose  extremity  marked  b  is 
the  north  pole,  and  a  the  south.  In  all  these  posi- 
tions, the  extremity  b  of  the  needle  is  directed  to- 
wards the  pole  A  of  the  loadstone  ;  and  the  extrem- 
ity a  to  the  pole  B.  The  point  c  indicates  the  pivot 
on  which  the  needle  revolves ;  and  you  have  only  to 
consider  the  figure  with  some  attention  in  order  to 
determine  what  situation  the  needle  will  assume,  in 
whatever  position  round  the  loadstone  the  pivot  c  is 
fixed. 

If  there  were,  therefore,  anywhere  a  very  large 
loadstone  AB,  the  magnetic  needles  placed  round  it 
would  assume  at  every  place  a  certain  situation,  as 
we  see  actually  to  be  the  case  round  the  globe. 
Now  if  the  globe  itself  were  that  loadstone,  we  should 
comprehend  why  the  magnetic  needles  everywhere 
assumed  a  certain  direction.  Naturalists,  accord- 
ingly, in  order  to  explain  this  phenomenon,  maintain 
that  the  whole  globe  has  the  property  of  a  magnet, 
or  that  we  ought  to  consider  it  as  a  prodigious  load- 
stone. Some  of  them  allege,  that  there  is  at  the 
centre  of  the  earth  a  very  large  loadstone,  which  has 
exercised  its  influence  on  all  the  magnetic  needles, 
and  even  on  all  the  loadstones,  which  are  to  be 
found  on  the  surface  of  the  earth;  and  that  it  is  this 
influence  which  directs  them  in  every  place,  con- 
formably to  the  directions  which  we  observe  them 
to  assume. 

But  there  is  no  occasion  to  have  recourse  to  a 
loadstone  concealed  in  the  bowels  of  the  earth.  Its 
surface  is  so  replenished  with  mines  of  iron  and 
loadstone,  that  their  united  force  may  well  supply 
the  want  of  this  huge  magnet.  In  fact,  all  loadstones 
are  extracted  from  mines — an  infallible  proof  that 
these  substances  are  found  in  great  abundance  in  the 
bowels  of  the  earth,  and  that  the  union  of  all  their 
powers  furnishes  the  general  force  which  produces 


ON  THE  MAGNETIC  NEEDLE.        203 

all  the  magnetical  phenomena.  We  are  likewise 
enabled  thereby  to  explain  why  the  magnetic  decli- 
nation changes,  with  time,  at  the  same  place ;  for 
it  is  well  known  that  mines  of  every  kind  of  metal 
are  subject  to  perpetual  change,  and  particularly 
those  of  iron,  to  which  the  loadstone  is  to  be  re- 
ferred. Sometimes  iron  is  generated,  and  sometimes 
it  is  destroyed  at  one  and  the  same  place  ;  there  are 
accordingly  at  this  day  mines  of  iron  where  there 
were  none  formerly;  and  where  it  was  formerly 
found  in  great  abundance  there  are  now  hardly  any 
traces  of  it.  This  is  a  sufficient  proof  that  the  total 
mass  of  loadstones  contained  in  the  earth  is  under- 
going very  considerable  changes,  and  thereby  un- 
doubtedly the  poles,  by  which  the  magnetic  declina- 
tion is  regulated,  likewise  change  with  the  lapse  of 
time. 

Here,  then,  we  must  look  for  the  reason  why  the 
magnetic  declination  is  subject  to  changes  so  con- 
siderable at  the  same  place  of  the  globe.  But  this 
very  reason,  founded  on  the  inconstancy  of  what  is 
passing  in  its  bowels,  affords  no  hope  of  our  ever 
being  able  to  ascertain  the  magnetic  declination  be- 
forehand, unless  we  could  find  the  means  of  subject- 
ing the  changes  of  the  earth  to  some  fixed  law.  A 
long  series  of  observations,  carried  on  through 
several  ages  successively,  might  possibly  throw 
some  light  on  the  subject. 

20th  October,  1761. 


LETTER  LIX. 

Elucidations  respecting  the  Cause  and  Variation  of  the 
Declination  of  Magnetic  Needles. 

THOSE  who  allege  that  the  earth  contains  in  its 
womb  a  prodigious  loadstone,  like  a  stone  with  a 
kernel  in  fruit,  are  under  the  necessity  of  admitting, 


204        ON  THE  MAGNETIC  NEEDLE. 

in  order  to  explain  the  magnetic  declination,  that  this 
stone  is  successively  shifting  its  situation.  It  must 
in  that  case  be  detached  from  the  earth  in  all  its 
parts ;  and  as  its  motion  would  undoubtedly  follow 
a  certain  law,  we  might  flatter  ourselves  with  the 
hope  of  one  day  discovering  it.  But  whether  there 
be  such  a  magnetic  stone  within  the  earth,  or  whether 
the  loadstones  scattered  up  and  down  through  its 
entrails  unite  their  force  to  produce  the  magnetical 
phenomena,  we  may  always  consider  the  earth  itself 
'as  a  loadstone,  in  subserviency  to  which  every  par- 
ticular loadstone,  and  all  magnetic  needles,  assume 
their  direction. 

Certain  naturalists  have  enclosed  a  very  powerful 
magnet  in  a  globe,  and  having  placed  a  magnetic 
needle  on  its  surface,  observed  phenomena  similar 
to  those  which  take  place  on  the  globe  of  the  earth, 
by  placing  the  magnet  within  the  globe  in  several 
different  positions.  Now,  considering  the  earth  as  a 
loadstone,  it  will  have  its  magnetic  poles,  which  must 
be  carefully  distinguished  from  the  natural  poles 
round  which  it  revolves.  These  poles  have  nothing 
in  common  between  them  but  the  name ;  but  it  is 
from  the  position  of  the  magnetic  poles  relatively 
to  the  natural  that  the  apparent  irregularities  in  the 
magnetic  declination  proceed,  and  particularly  of 
the  lines  traced  on  the  globe,  of  which  I  have  en- 
deavoured to  give  you  some  account. 

In  order  more  clearly  to  elucidate  this  subject,  I 
remark,  that  if  the  magnetic  poles  exactly  coincided 
with  the  natural,  there  would  be  no  declination  all 
over  the  earth  ;  magnetic  needles  would  universally 
point  to  the  north  precisely,  and  their  position  would 
be  exactly  that  of  the  meridian  line.  This  would  no 
doubt  be  an  unspeakable  advantage  in  navigation,  as 
we  should  then  know  with  precision  the  course  of 
the  vessel  and  the  direction  of  the  wind ;  whereas 
at  present  we  must  always  look  for  the  declination 
of  the  compass  before  we  are  able  to  determine  the 


ON  THE  MAGNETIC  NEEDLE.        205 

true  quarters  of  the  world.  But  then  the  compass 
could  furnish  no  assistance  towards  ascertaining  the 
longitude,  an  object  which  the  declination  may  sooner 
or  later  render  attainable. 

Hence  it  may  be  concluded,  that  if  the  magnetic 
poles  of  the  earth  differed  very  greatly  from  the 
natural,  and  that  if  they  were  directly  opposite  to 
each  other — which  would  be  the  case  if  the  mag- 
netic axis  of  the  earth,  that  is,  the  straight  line 
drawn  from  the  one  magnetic  pole  to  the  other, 
passed  through  the  centre  of  the  earth — then  mag- 
netic needles  would  universally  point  towards  these 
magnetic  poles,  and  it  would  be  easy  to  assign  the 
magnetic  direction  proper  to  every  place ;  we  should 
only  have  to  draw  for  every  place  a  circle  which 
should  at  the  same  time  pass  through  the  two  mag- 
netic poles,  and  the  angle  which  this  circle  would 
make  with  the  meridian  of  the  same  place  must  give 
the  magnetic  declination. 

In  this  case,  the  two  lines  under  which  there  is  no 
declination  would  be  the  meridians  drawn  through 
the  magnetic  poles.  But  as  we  have  seen  that,  in 
reality,  these  two  lines  without  declination  are  not 
meridians,  but  take  a  very  unaccountable  direction, 
it  is  evident  that  no  such  case  actually  takes  place. 
Halley  clearly  saw  this  difficulty,  and  therefore 
thought  himself  obliged  to  suppose  a  double  load- 
stone in  the  bowels  of  the  earth,  the  one  fixed,  the 
other  moveable  ;  of  consequence,  he  was  obliged  to 
admit  four  poles  of  the  earth,  two  of  them  towards 
the  north  and  two  towards  the  south,  at  unequal  dis- 
tances. But  this  hypothesis  seems  to  me  rather  a 
bold  conjecture :  it  by  no  means  follows,  that  be- 
cause these  lines  of  no  declination  are  not  meridians, 
there  must  be  four  magnetic  poles  on  the  earth ;  but 
rather,  that  there  are  only  two,  which  are  not  directly 
opposite  to  each  other ;  or,  which  comes  to  the  same 
thing,  that  the  magnetic  axis  does  not  pass  through 
the  centre  of  the  earth. 

VOL.  II— S 


206       ON  THE  MAGNETIC  NEEDLE. 

It  remains,  therefore,  that  we  consider  the  cases 
in  which  these  two  magnetic  poles  are  not  directly 
opposite,  and  in  which  the  magnetic  axis  does  not 
pass  through  the  centre  of  the  earth ;  for  if  we  em- 
brace the  hypothesis  of  the  magnetic  nucleus  within 
the  earth,  why  should  one  of  its  poles  be  precisely 
opposite  to  the  other?  This  nucleus  may  very 
probably  be  not  exactly  in  the  very  centre  of  the 
earth,  but  at  a  considerable  distance  from  it.  Now, 
if  the  magnetic  poles  are  not  diametrically  opposite 
to  each  other,  the  lines  of  no  declination  may  actually 
assume  a  direction  similar  to  that  which,  from  ob- 
servation, we  find  they  do ;  it  is  even  possible  to 
assign  to  the  two  magnetic  poles  such  places  on  the 
earth,  that  not  only  these  lines  should  coincide  with 
observation,  but  likewise,  for  every  degree  of  decli- 
nation, whether  western  or  eastern,  we  may  find 
lines  precisely  similar  to  those  which  at  first  seemed 
so  unaccountable. 

In  order,  then,  to  know  the  state  of  magnetic 
declination,  all  that  is  requisite  is  to  fix  the  two 
magnetic  poles ;  and  then  it  becomes  a  problem  in 
geometry  to  determine  the  direction  of  all  the  lines 
which  I  mentioned  in  my  preceding  Letter,  drawn 
for  every  place  where  the  declination  is  the  same : 
by  such  means,  too,  we  should  be  enabled  to  rectify 
these  lines,  and  to  fill  up  the  countries  where  no 
observations  have  been  made ;  and  were  it  possible 
to  assign,  for  every  future  period,  the  places  of  the 
two  magnetic  poles  on  the  globe,  it  would  undoubt- 
edly prove  the  most  satisfactory  solution  of  the 
problem  of  the  longitude. 

There  is  no  occasion,  therefore,  for  a  double  load- 
stone within  the  earth,  or  for  four  magnetic  poles,  in 
order  to  explain  the  decimation  of  magnetic  needles, 
as  Halley  supposed ;  but  for  a  simple  magnet,  or  two 
magnetic  poles,  provided  its  just  place  is  assigned  to 
each.*  It  appears  to  me,  that,  from  this  reflection, 

*  The  phenomena  render  it  absolutely  necessary  to  admit  two  mag- 


ON  THE  MAGNETIC  NEEDLE.        207 

we  are  much  more  advanced  in  our  knowledge  of 
magnetism. 

October,  1761. 


LETTER  LX. 

Inclination  or  Dip  of  Magnetic  Needles. 

You  will  please  to  recollect,  that  on  rubbing  a 
needle  against  the  loadstone,  it  acquires  not  only  the 
property  of  pointing  towards  a  certain  point  of  the 
horizon,  but  that  its  northern  extremity  sinks,  as  if 
it  had  become  heavier,  which  obliges  us  to  diminish 
its  weight  somewhat,  or  to  increase  that  of  the  other 
extremity,  in  order  to  restore  the  equilibrium.  I 
have,  without  putting  this  in  practice,  made  several 
experiments  to  ascertain  how  far  the  magnetic  force 
brought  down  the  northern  extremity  of  the  magnet- 
ized needle,  and  I  have  found  that  it  sank  so  as  to 
make  an  ang-le  of  72  degrees  with  the  horizon,  and 
that  in  this  situation  the  needle  remained  at  rest.  It 
is  proper  to  remark,  that  these  experiments  were 
made  at  Berlin  about  six  years  ago ;  for  I  shall  show 
you  afterward,  that  this  direction  to  a  point  below 
the  horizon  is  as  variable  as  the  magnetic  declina- 
tion. 

Hence  we  see  that  the  magnetic  power  produces  a 
double  effect  on  needles ;  the  one  directs  the  needle 

netic  poles.  The  two  northern  poles,  which  we  may  call  B  and  b,  and 
the  two  southern  poles,  A  and  a,  were  thus  situated,  according  to  Hans- 
teen,  in  1823. 

North  Lat.  West  Long. 

B  in  69«  34'  and     271°  38'  from  Greenwich. 
b       85     9  142    11 

A      68    48  132    11 

a       78   23  223     8 

The  pole  B  moves  round  the  north  pole  of  the  globe  in  1740. 

ft,  which  is  weaker  vhan  B,  in  860. 

A  moves  round  the  south  pole  of  the  globe  in  4609. 

a,  which  is  weaker  than  A,  in  1304. 

See  the  Edinburgh  Philosophical  Journal,  vol.  iv.  p.  117.— Ed, 


208        ON  THE  MAGNETIC  NEEDLE. 

towards  a  certain  quarter  of  the  horizon,  the  devia- 
tion of  which  from  the  meridian  line  is  what  we 
call  the  magnetic  declination ;  the  other  impresses  on 
it  an  inclination  towards  the  horizon,  sinking  the  one 
or  the  other  extremity  under  it  up  to  a  certain  angle. 

Let  d  e,  Fig.  112,  be  the  hori-  „. 

zontal  line,  drawn  according  to 
the   magnetic   declination,    and 
the  needle  will  assume,  at  Ber- 
lin,  the    situation   b  a,   which 
makes  with  the  horizon  d  e  the 
angle  d  c  b,  or  e  c  a,  which  is 
72°,  and  consequently  with  the 
vertical  /  g  an  angle  b  c  g,  or 
a  c/,  of  18°.     This  second  effect 
of  the  magnetic  force,  by  which 
the    magnetic    needle    affects   a    certain    inclina- 
tion towards  the  horizon,  is  as  remarkable  as  the 
first ;  and  as  the  first  is  denominated  the  magnetic 
declination,  the  second  is  known  by  the  name  of 
magnetic  inclination  or  dip,  which  deserves,  as  well 
as  the  declination,  to  be  everywhere  observed  with 
all  possible  care,  as  we  find  in  it  a  similar  variation. 
The  inclination  at  Berlin  has  been  found  72°,*  at 
Basle  only  70°,  the  northern  extremity  of  the  needle 
being  sunk,  and  the  opposite,  of  consequence,  raised 
to  that  angle.    This  takes  place  in  countries  which 
are  nearer  to  the  northern  magnetic  pole  of  the 
earth;  and  in  proportion  as  we   approach  it,  the 
greater  becomes  the  inclination  of  the  magnetic 
needle,  or  the  more  it  approaches  the  vertical  line  ; 
so  that  if  we  could  reach  the  magnetic  pole  itself, 
the  needle  would  there  actually  assume  a  vertical 
situation ;  its  northern  extremity  pointing  perpen- 
dicularly downwards,  and  its  southern  end  upwards. f 

*  In  1805,  it  was  found  by  Humboldt  to  be  69°  53'  at  Berlin.— Ed. 

t  On  the  18th  July.  1820,  the  inclination  of  the  needle  was  observed 
by  Mr.  Sabine  to  be  &8°  43'  5"  at  Winter  Harbour  in  Melville  Island,  in 
west  longitude  110°  48',  and  74°  47'  of  north  latitude.— Ed. 


ON  THE  MAGNETIC  NEEDLE.        209 

The  farther,  on  the  contrary,  you  remove  from  the 
northern  magnetic  pole  of  the  earth,  and  approach 
the  southern,  the  more  the  inclination  diminishes; 
it  will  at  length  disappear,  and  the  needle  will  assume 
a  horizontal  position,  when  equally  distant  from  both 
poles ;  but  in  proceeding  towards  the  south  pole  of 
the  earth,  the  southern  extremity  of  the  needle  will 
sink  more  and  more  under  the  horizon,  the  northern 
extremity  rising  in  proportion,  till  at  the  pole  itself 
the  needle  again  becomes  vertical,  with  the  south- 
ern extremity  perpendicularly  downwards,  and  the 
northern  upwards. 

It  were  devoutly  to  be  wished  that  experiments 
had  been  as  carefully  and  as  generally  made,  with 
the  view  of  ascertaining  the  magnetic  inclination  as 
of  determining  the  declination ;  but  this  important 
article  of  experimental  philosophy  has  hitherto  been 
too  much  neglected,  though  certainly  neither  less 
curious  nor  less  interesting  than  that  of  the  declina- 
tion. This  is  not,  however,  a  matter  of  surprise : 
experiments  of  this  sort  are  subject  to  too  many 
difficulties ;  and  almost  all  the  methods  hitherto  at- 
tempted of  observing  the  magnetic  inclination  have 
failed.  One  artist  alone,  Mr.  Diterich,  of  Basle,  has 
succeeded,  having  actually  constructed  a  machine 
proper  for  the  purpose,  under  the  direction  of  the 
celebrated  Mr.  Daniel  Bemouilli.  He  sent  me  two 
of  the  machines,  by  means  of  which  I  have  observed, 
at  Berlin,  this  inclination  of  72  degrees ;  and  how- 
ever curious  in  other  respects  the  English  and 
French  may  be  in  prosecuting  such  inquiries,  they 
have  put  no  great  value  on  Mr.  DitericWs  machine, 
though  it  is  the  only  one  adapted  for  this  purpose.* 

*  One  of  the  simplest  machines  for  measuring  the  dip  of  the  needle  is 
Copt.  Scoresby's  magnetimeter.  A  bar  of  iron  deprived  entirely  of  its 
magnetism,  either  by  heat,  or  by  hammering  it  in  the  magnetic  equator, 
is  placed  in  the  magnetic  meridian,  upon  an  inclined  plane.  This  plane 
is  raised  or  depressed  by  a  wheel  and  pinion,  till  the  iron  bar  exercises 
no  action  whatever  upon  a  compass-needle  placed  near  it.  When  this 
happens,  the  bar  is  in  the  magnetic  equator,  and  consequently  the  com- 
S2 


210        ON  THE  MAGNETIC  NEEDLE. 

This  instance  demonstrates  how  the  progress  of 
science  may  be  obstructed  by  prejudice ;  hence 
Berlin  and  Basle  are  the  only  two  places  on  the 
globe  where  the  magnetic  inclination  is  known. 

Needles  prepared  for  the  construction  of  com- 
passes are  by  no  means  proper  to  indicate  the  quan- 
tity of  magnetic  inclination,  though  they  may  convey 
a  rough  idea  of  its  effect,  because  the  northern  ex- 
tremity in  these  latitudes  becomes  heavier.  In  order 
to  render  serviceable  needles  intended  to  discover 
the  declination,  we  are  under  the  necessity  of  de- 
stroying the  effect  of  the  inclination,  by  diminishing 
the  weight  of  the  northern  extremity,  or  increasing 
that  of  the  southern.  To  restore  the  needle  to  a 
horizontal  position,  the  last  of  these  methods  is 
usually  employed,  and  a  small  morsel  of  wax  is 
affixed  to  the  southern  extremity  of  the  needle. 
You  are  abundantly  sensible  that  this  remedy  applies 
only  to  these  regions  of  the  globe  where  the'incli- 
natory  power  is  so  much,  and  no  more ;  and  that 
were  we  to  travel  with  such  a  needle  towards  the 
northern  magnetic  pole  of  the  earth,  the  incjinatory 
power  would  increase,  so  that  to  prevent  the  effect 
we  should  be  obliged  to  increase  the  quantity  of 
wax  at  the  southern  extremity.  But  were  we  travel- 
ling southward,  and  approaching  the  opposite  pole 
of  the  earth,  where  the  inclinatory  power  on  the 
northern  extremity  of  the  needle  diminishes,  the 
quantity  of  wax  affixed  to  the  other  extremity  -must 
then  likewise  be  diminished ;  after  that  it  must  be 
taken  away  altogether,  being  wholly  useless  when 
we  arrive  at  places  where  the  magnetic  inclination 
disappears.  On  proceeding  still  forward  to  the  south 
pole,  the  southern  extremity  of  the  needle  sinks ;  so 

plement  of  the  inclination  of  the  plane  on  which  it  rests  is  the  dip  or 
inclination  of  the  needle  at  the  place  where  the  observation  is  made. 
This  angle  of  inclination  was  measured  by  a  vertical  graduated  circle, 
adjusted  to  zero  when  the  bar  had  a  horizontal  position. — See  the  Edin- 
burgh Transactions,  vol.  ix.,  and  the  Edinburgh  Philosophical  Journal, 
rol.  ix.  p.  42,  for  a  full  account  of  this  instrument.— Ed. 


MAGNETIC    POWER.  211 

that  to  remedy  this,  a  morsel  of  wax  must  be  affixed 
to  the  northern  extremity  of  the  needle.  Such  are 
the  means  employed  in  long  voyages  to  preserve 
the  compass  in  a  horizontal  position. 

In  order  to  observe  the  magnetic  inclination,  it 
would  be  necessary  to  have  instruments  made  on 
purpose,  similar  to  that  invented  by  the  artist  of 
Basle.  His  instrument  is  called  the  inclinatory ;  but 
there  is  little  appearance  of  its  coming  into  general 
use.  It  is  still  less  to  be  expected  that  we  should 
soon  have  charts  constructed  with  the  magnetic  in- 
clination, similar  to  those  which  represent  the  decli- 
nation. The  same  method  might  easily  be  followed, 
by  drawing  lines  through  all  the  places  where  the 
magnetic  inclination  is  the  same :  so  that  we  should 
have  lines  of  no  inclination ;  afterward  other  lines 
where  the  inclination  would  be  5°,  10°,  15°,  20°,  and 
so  on,  whether  northward  or  southward.* 

27th  October,  1761. 


LETTER  LXI. 

True  Magnetic  Direction ;  subtile  Matter  which 
produces  the  Magnetic  Power. 

IN  order  to  form  a  just  idea  of  the  effect  of  the 
earth's  magnetic  power,  we  must  attend  at  once  to 
the  declination  and  inclination  of  the  magnetic 
needle,  at  every  place  of  the  globe.  At  Berlin,  we 
know  the  declination  is  15°  west,  and  the  inclination 
of  the  northern  extremity  72°.  On  considering 
this  double  effect,  the  declination  and  inclination, 
we  shall  have  the  true  magnetic  direction  for  Berlin. 
We  draw  first,  on  a  horizontal  plane,  a  line  which 
shall  make  with  the  meridian  an  angle  of  15°  west, 
and  thence  descending  towards  the  vertical  line,  we 

*  See  Note  on  I/etter  LVI. 


212  MAGNETIC    POWER. 

trace  a  new  line,  which  shall  make  with  it  an  angle 
of  72°  ;  and  this  will  give  us  the  magnetic  direction 
for  Berlin :  from  which  you  will  comprehend  how 
the  magnetic  direction  for  every  other  place  is  to 
be  ascertained,  provided  the  inclination  and  declina- 
tion are  known. 

Every  magnet  exhibits  phenomena  altogether 
similar.  You  have  only  to  place  one  on  a  table 
covered  with  filings  of  steel,  and  you  will  see  the 
filings  arrange  themselves  round  the  loadstone  A  B, 
nearly  as  represented  in  Fig.  113, 
in  which  every  particle  of  the 
filings  may  be  considered  as  a 
small  magnetic  needle,  indicating 
at  every  point  round  the  load- 
stone the  magnetic  direction. 
This  experiment  leads  us  to  in- 
quire into  the  cause  of  all  these 
phenomena. 

The  arrangement  assumed  by  the  steel  filings 
leaves  no  room  to  doubt  that  it  is  a  subtile  and 
invisible  matter  which  runs  through  the  particles  of 
the  steel,  and  disposes  them  in  the  direction  which 
we  here  observe.  It  is  equally  clear  that  this  sub- 
tile matter  pervades  the  loadstone  itself,  entering  at 
one  of  the  poles,  and  going  out  at  the  other,  so  as 
to  form,  by  its  continual  motion  round  the  loadstone, 
a  vortex  which  reconducts  the  subtile  matter  from 
one  pole  to  the  other ;  and  this  motion  is,  without 
doubt,  extremely  rapid. 

The  nature  of  the  loadstone  consists,  then,  in  a 
continual  vortex,  which  distinguishes  it  from  all 
other  bodies ;  and  the  earth  itself,  in  the  quality  of 
a  loadstone,  must  be  surrounded  with  a  similar  vor- 
tex, acting  everywhere  on  magnetic  needles,  and 
making  continual  efforts  to  dispose  them  according 
to  its  own  direction,  which  is  the  same  I  formerly 
denominated  the  magnetic  direction :  this  subtile 
matter  is  continually  issuing  at  one  of  the  magnetic 


MAGNETIC    POWER.  213 

poles  of  the  earth,  and  after  having  performed  a 
circuit  round  to  the  other  pole,  it  there  enters,  and 
pervades  the  globe  through  and  through  to  the  oppo- 
site pole,  where  it  again  escapes. 

We  are  not  yet  enabled  to  determine  by  which  of 
the  two  magnetic  poles  of  the  earth  it  enters  or 
issues ;  the  phenomena  depending  on  this  have  suph 
a  perfect  resemblance,  that  they  are  indistinguishable. 
It  is  undoubtedly,  likewise,  this  general  vortex  of 
the  globe  which  supplies  the  subtile  matter  of  every 
particular  loadstone  to  magnetic  iron  or  steel,  and 
which  keeps  up  the  particular  vortices  that  surround 
them. 

Previous  to  a  thorough  investigation  of  the  nature 
of  this  subtile  matter,  and  its  motion,  it  must  be  re- 
marked, that  its  action  is  confined  to  loadstone,  iron, 
and  steel  ;*  all  other  bodies  are  absolutely  indifferent 
to  it :  the  relation  which  it  bears  to  those  must 
therefore  be  by  no  means  the  same  which  it  bears  to 
others.  We  are  warranted  to  maintain,  from  mani- 
fold  experiments,  that  this  subtile  matter  freely  per- 
vades all  other  bodies,  and  even  in  all  directions; 
for  when  a  loadstone  acts  upon  a  needle,  the  action 
is  perfectly  the  same  whether  another  body  inter- 
poses or  not,  provided  the  interposing  body  is  not 
iron,  and  its  action  is  the  same  on  the  filings  of  iron. 
This  subtile  matter,  therefore,  must  pervade  all 
bodies,  iron  excepted,  as  freely  as  it  does  air,  and 
even  pure  ether;  for  these  experiments  succeed 
equally  well  in  a  receiver  exhausted  by  the  air-pump. 
This  matter  is  consequently  different  from  ether, 
and  even  much  more  subtile.  And,  on  account  of 
the  general  vortex  of  the  earth,  it  may  be  affirmed 
that  the  globe  is  completely  surrounded  by  it,  and 

*  Professor  Hansteen  has  lately  found  that  every  vertical  object,  of 
whatever  materials  it  is  composed,  has  a  magnetic  south  pole  above,  and 
a  magnetic  north  pole  below.  This  curious  fact  he  has  put  beyond  a 
doubt,  by  measuring  the  velocity  of  the  oscillations  of  a  magnetic  needle 
on  different  sides  of  the  extremities  of  the  vertical  object.— See  the  Edin- 
burgh Philosophical  Journal,  vol.  iv.  p.  299,  300. — Ed. 


214      NATURE  OF  MAGNETIC  MATTER. 

freely  pervaded,  as  all  other  bodies  are,  excepting 
the  loadstone  and  iron ;  for  this  reason  iron  and 
steel  may  be  denominated  magnetic  bodies,  to  dis- 
tinguish them  from  others. 

But  if  this  magnetic  matter  passes  freely  through 
all  non-magnetic  bodies,  what  relation  can  it  have  to 
those  which  are  such  1  We  have  just  observed,  that 
the  magnetic  vortex  enters  at  one  of  the  poles  of 
every  loadstone,  and  goes  out  at  the  other ;  whence 
it  may  be  concluded  that  it  freely  pervades  load- 
stones likewise,  which  would  not  distinguish  them 
from  other  bodies.  But  as  the  magnetic  matter 
passes  through  the  loadstone  only  from  pole  to  pole, 
this  is  a  circumstance  very  different  from  what  takes 
place  in  others.  Here,  then,  we  have  the  distinctive 
character.  Non-magnetic  bodies  are  freely  pervaded 
by  the  magnetic  matter  in  all  directions :  loadstones 
are  pervaded  by  it  in  one  direction  only ;  one  of  the 
poles  being  adapted  to  its  admission,  the  other  to 
its  escape.  But  iron  and  steel,  when  rendered 
magnetic,  fulfil  this  last  condition ;  when  they  are 
not,  it  may  be  affirmed  that  they  do  not  grant  a 
free  transmission  to  the  magnetic  matter  in  any 
direction. 

This  may  appear  strange,  as  iron  has  open  pores, 
which  transmit  the  ether,  though  it  is  not  so  subtile 
as  the  magnetic  matter.  But  we  must  carefully  dis- 
tinguish a  simple  passage,  from  one  in  which  the 
magnetic  matter  may  pervade  the  body,  with  all  its 
rapidity,  without  encountering  any  obstacle. 

31  si  October,  1761. 


LETTER  LXII. 

Nature  of  the  Magnetic  Matter^  and  of  its  rapid  Current. 
Magnetic  Canals. 

I  AM  very  far  from  pretending  to  explain  perfectly 
the  phenomena  of  magnetism ;  it  presents  difficulties 


NATURE  OF  MAGNETIC  MATTER.      215 

which  I  did  not  find  in  those  of  electricity.  The 
cause  of  it  undoubtedly  is,  that  electricity  consists  in 
too  great  or  too  small  a  degree  of  compression  of  a 
subtile  fluid  which  occupies  the  pores  of  bodies, 
without  supposing  that  subtile  fluid,  which  is  the 
ether,  to  be  in  actual  motion :  but  magnetism  cannot 
be  explained  unless  we  suppose  a  vortex  in  rapid 
agitation,  which  penetrates  magnetic  bodies. 

The  matter  which  constitutes  these  vortices  is 
likewise  much  more  subtile  than  ether,  and  freely 
pervades  the  pores  of  loadstones,  which  are  imper- 
vious even  to  ether.  Now,  this  magnetic  matter  is 
diffused  through  and  mixed  with  the  ether,  as  the 
ether  is  with  gross  air ;  or,  just  as  ether  occupies 
and  fills  up  the  pores  of  air,  it  may  be  affirmed  that 
the  magnetic  matter  occupies  and  fills  the  pores  of 
ether. 

I  conceive,  then,  that  the  loadstone  and  iron  have 
pores  so  small  that  the  ether  in  a  body  cannot  force 
its  way  into  them,  and  that  the  magnetic  matter 
alone  can  penetrate  them  :  and  which,  on  being  ad- 
mitted, separates  itself  from  the  ether  by  what  may 
be  called  a  kind  of  filtration.  In  the  pores  of  the 
loadstone  alone,  therefore,  is  the  magnetic  matter  to 
be  found  in  perfect  purity:  everywhere  else  it  is 
blended  with  ether,  as  this  last  is  with  the  air. 

You  can  easily  imagine  a  series  of  fluids,  one 
always  more  subtile  than  another,  and  which  are 
perfectly  blended  together.  Nature  furnishes  in- 
stances of  this.  Water,  we  know,  contains  in  its 
pores  particles  of  air,  which  are  frequently  seen 
discharging  themselves  in  the  form  of  small  bubbles : 
air  again,  it  is  equally  certain,  contains  in  its  pores  a 
fluid  incomparably  more  subtile — namely,  ether — and 
which  on  many  occasions  is  separated  from  it,  as  in 
electricity.  And  now  we  see  a  still  further  progres- 
sion, and  that  ether  contains  a  matter  much  more 
subtile  than  itself — the  magnetic  matter — which  may 


216 


NATURE  OF  MAGNETIC  MATTER. 


perhaps  contain,  in  its  turn,  others  still  more  subtile, 
at  least  this  is  not  impossible. 

Having  considered  the  nature  of  this  magnetic 
matter,  let  us  see  how  the  phenomena  are  produced.  I 
consider  a  loadstone,  then ;  and  say,  first,  that  besides 
a  great  many  pores  filled  with  ether,  like  all  other 
bodies,  it  contains  some  still  much  more  narrow,  into 
which  the  magnetic  matter  alone  can  find  admission. 
Secondly,  these  pores  are  disposed  in  such  a  manner 
as  to  have  a  communication  with  each  other,  and 
constitute  tubes  or.  canals,  through  which  the  mag- 
netic matter  passes  from  the  one  extremity  to  the 
other.  Finally,  this  matter  can  be  transmitted  through 
these  tubes  only  in  one  direction,  without  the  possi- 
bility of  returning  in  an  opposite  direction.  This 
most  essential  circumstance  requires  a 
more  particular  elucidation.  Fig.  114. 

First,  then,  I  remark,  that  the  veins 
and  lymphatic  vessels  in  the  bodies  of 
animals  are  tubes  of  a  similar  con- 
struction, containing  valves,  represented 
in  Fig.  114,  by  the  strokes  m  n,  which, 
by  raising  themselves,  grant  a  free  pas- 
sage to  the  blood  when  it  flows  from 
A  to  B,  and  to  prevent  its  reflux  from  B 
to  A.  For  if  the  blood  attempted  to  flow 
from  B  to  A,  it  would  press  down  the 
moveable  extremity  of  the  valve  m  on  the 
side  of  the  vein  o,  and  totally  obstruct 
the  passage.  Valves  are  thus  employed 
in  aqueducts,  to  prevent  the  reflux  of  the 
water.  I  do  not  consider  myself,  then, 
as  supposing  any  thing  contrary  to  nature, 
when  I  say  that  the  canals  in  loadstones, 
which  admit  the  magnetic  matter  only, 
sire  of  the  same  construction. 


Jffi 


NATURE  OF  MAGNETIC  MATTER.      217 

Fig.  115,  represents  this  magnetic  canal,  Fig.  115. 
according  to  my  idea  of  it.     I  conceive  it 
furnished  inwardly  with  bristles  directed 


from  A  towards  B,  which  present  no  oppo- 


\o/ 


V 
n 

v 

n 

V 

n 
V 


sition  to  the  magnetic  matter  in  its  passage 
from  A  to  B,  for  in  this  case  they  open  of 
themselves  at  n,  to  let  the  matter  pass  at 
o;  but  they  would  immediately  obstruct  the 
channel  were  it  to  attempt  a  retrograde 
course  from  B  to  A.  The  nature  of  mag- 
netic canals  consists,  then,  in  granting 
admission  to  the  magnetic  matter  only  at 
A.,  to  flow  towards  B,  without  the  possi- 
bility of  returning  in  the  opposite  direction 
from  B  towards  A. 

This  construction  enables  us  to  explain 
how  the  magnetic  matter  enters  into  these 
tubes,  and  flies  through  them  with  the  great- 
est rapidity,  even  when  the  whole  ether  is 
in  a  state  of  perfect  rest,  which  is  the  most 
surprising ;  for  how  can  a  motion  so  rapid  be 
produced  1  This  will  appear  perfectly  clear 
to  you,  if  you  will  please  to  recollect  that  ether  is  a 
matter  extremely  elastic ;  accordingly,  the  magnetic 
matter,  which  is  scattered  about,  will  be  pressed  by 
it  on  every  side.  Let  us  suppose  the  magnetic  canal 
A  B  still  quite  empty,  and  that  a  particle  of  magnetic 
matter  m  presents  itself  at  the  entrance  A ;  and  this 
particle  pressed  on  every  side  at  the  opening  of  the 
canal,  into  which  the  ether  cannot  force  admission, 
it  will  there  be  pressed  forward  with  prodigious  force, 
and  enter  into  the  canal  with  equal  rapidity :  another 
particle  of  magnetic  matter  will  immediately  present 
itself,  and  be  driven  forward  with  the  same  force ; 
and  in  like  manner  all  the  following  particles.  There 
will  thence  result  a  continual  flux  of  magnetic  matter, 
which,  meeting  with  no  obstruction  in  this  canal, 
will  escape  from  it  at  B  with  the  same  rapidity  that 
it  enters  at  A. 

VOL.  II.— T 


218  ACTION    OF   MAGNETS 

My  idea  then  is,  that  every  loadstone  contains  a 
great  multitude  of  these  canals,  which  I  denominate 
magnetic ;  and  it  very  naturally  follows,  that  the 
magnetic  matter  dispersed  in  the  ether  must  enter 
into  them  at  one  extremity,  and  escape  at  the  other, 
with  great  impetuosity;  that  is,  we  shall  have  a  per- 
petual current  of  magnetic  matter  through  the  canals 
of  the  loadstone  :  and  thus  I  hope  I  have  surmounted 
the  greatest  difficulties  which  can  occur  in  the  theory 
of  magnetism. 

3d  November,  1761. 


LETTER  LXIII. 

Magnetic  Vortex.     Action  of  Magnets  upon  each  other. 

You  have  now  seen  in  what  the  distinctive  character 
of  the  loadstone  consists ;  and  that  each  contains 
several  canals,  of  which  I  have  attempted  to  give  a 
description. 

Fig.  116  represents  a  loadstone  Fig.  116. 
A  B,  with  three  magnetic  canals 
a  b,  through  which  the  magnetic 
matter  will  flow  with  the  utmost 
rapidity,  entering  at  the  extremi- 
ties marked  a,  and  escaping  at 
those  marked  b :  it  will  escape 
indeed  with  the  same  rapidity; 
but  immediately  meeting  with  the 
ether  blended  with  the  grosser  air, 
great  obstructions  will  oppose  the  continuation  of  its 
motion  in  the  same  direction ;  and  not  only  will  the 
motion  be  retarded,  but  its  direction  diverted  towards 
the  sides  c  c.  The  same  thing  will  take  place  at  the 
entrance,  towards  the  extremities  a  a  a ;  on  aecoimt 
of  the  rapidity  with  which  the  particles  of  magnetic 
matter  force  their  way  into  them,  the  circulation 
will  quickly  overtake  those  which  are  still  towards  the 


UPON    EACH    OTHER.  219 

sides  e  e,  and  these  in  their  turn  will  be  replaced  by 
those  which,  escaping  from  the  extremities  b  b  b, 
have  been  already  diverted  towards  c  c ;  so  that  the 
same  magnetic  matter  which  issued  from  the  ex- 
tremities bbb  quickly  returns  towards  those  marked 
a  a  a,  performing  the  circuit  b  c  d  e  a ;  and  this  cir- 
culation round  the  loadstone  is  what  we  call  the 
magnetic  vortex. 

It  must  not  be  imagined,  however,  that  it  is  always 
the  same  magnetic  matter  which  forms  these  vor- 
tices :  a  considerable  part  of  it  will  escape,  no  doubt, 
as  well  towards  B  as  towards  the  sides,  in  performing 
the  circuit ;  but  as  a  compensation,  fresh  magnetic 
matter  will  enter  by  the  extremities  a  a  a,  so  that  the 
matter  which  constitutes  the  vortex  is  succedaneous 
and  very  variable :  a  magnetic  vortex,  surrounding 
the  loadstone,  will,  however,  always  be  kept  up,  and 
produce  the  phenomena  formerly  observed  in  filings 
of  steel  scattered  round  the  loadstone. 

You  will  please  further  to  attend  to  this  circum- 
stance, that  the  motion  of  the  magnetic  matter  in 
the  vortex  is  incomparably  slower  out  of  the  load- 
stone than  in  the  magnetic  tubes,  where  it  is  sepa- 
rated from  the  ether,  after  having  been  forced  into 
them  by  all  the  elastic  power  of  this  last  fluid ;  and 
that  on  escaping  it  mixes  again  with  the  ether,  and 
thereby  loses  great  part  of  its  motion,  so  that  its 
velocity  in  travelling  to  the  extremities  aaais  incom- 
parably less  than  in  the  magnetic  canals  a  b,  though 
still  very  great  with  respect  to  us.  You  will  easily 
comprehend,  then,  that  the  extremities  of  the  mag- 
netic canals,  by  which  the  matter  enters  into  the 
loadstone  and  escapes  from  it,  are  what  we  call  its 
poles ;  and  that  the  magnetic  poles  of  a  loadstone 
are  by  no  means  mathematical  points,  the  whole 
space  in  which  the  extremities  of  the  magnetic  canals 
terminate  being  one  magnetic  pole,  as  in  the  load- 
stone represented  by  Fig.  113  (p.  212),  where  the 
whole  surfaces  A  and  B  are  the  two  poles. 


220  ACTION   OF   MAGNETS. 

Now,  though  these  poles  are  distinguished  by  the 
terms  north  and  south,  yet  we  cannot  affirm  with  cer- 
tainty whether  it  is  by  the  north  or  south  pole  that 
the  magnetic  matter  enters  into  loadstones.  You 
will  see,  in  the  sequel,  that  all  the  phenomena  pro- 
duced by  the  admission  and  escape  have  such  a  per- 
fect resemblance  that  it  appears  impossible  to  deter- 
mine the  question  by  experiments.  It  is  therefore 
a  matter  of  indifference  whether  we  suppose  that 
the  magnetic  matter  enters  or  escapes  by  the  north 
pole  or  by  the  south. 

Be  this  as  it  may,  I  shall  mark  with  the  letter  A 
the  pole  by  which  the  magnetic  matter  enters,  and 
with  B  that  by  which  it  escapes,  without  pretending 
thereby  to  indicate  which  is  north  or  south.  I  pro- 
ceed to  the  consideration  of  these  vortices,  in  order 
to  form  a  judgment  how  two  loadstones  act  upon 
each  other. 

Let  us  suppose  that  the  two  loadstones  A  B  and 
a  5,  Fig.  117,  are  presented  to  pio-,  117. 

each  other  by  the  poles  of  the      ^3--.* 
same  name  A,  a,  and  their     (  .  ( 

vortices  will  be  in  a  state  of   »£3ZZk*vt^      *!' 
total  opposition.     The  mag-     \  J  I 

netic  matter  which  is  at  C       ""~i; 
will  enter  at  A  and  a,  and  these 

two  vortices  attempting  mutually  to  destroy  each 
other,  the  matter  which  proceeds  by  E  to  enter  at  A 
will  meet  at  D  that  of  the  other  loadstone  returning 
by  e  to  enter  at  a:  from  this  must  result  a  collision 
of  the  two  vortices,  in  which  the  one  will  repel  the 
other ;  and  this  effect  will  extend  to  the  loadstones 
themselves,  which,  thus  situated,  undergo  mutual 
repulsion.  The  same  thing  would  take  place  if  the 
two  loadstones  presented  to  each  other  the  other 
poles  B  and  b :  for  this  reason  the  poles  of  the  same 
name  are  denominated  hostile,  because  they  actually 
repel  each  other. 

But  if  the  loadstones  present  to  each  other  tha 


MAGNETIC    FORCE.  221 

poles  of  a  different  name,  an  opposite  effect  will 
ensue,  and  you  will  perceive  that  they  have  a  mutual 
attraction. 

In  Fig.  118,  where  the 
two  loadstones  present  to 
each  other  the  poles  B  and 
a,  the  magnetic  matter 
which  issues  from  the  pole 
B,  finding  immediately  free 
admission  into  the  other 
loadstone  by  its  pole  a, 
will  not  be  diverted  towards  the  sides  in  order  to 
return  and  re-enter  at  A,  but  will  pass  directly  by  C 
into  the  other  loadstone,  and  escape  from  it  at  b,  and 
will  perform  the  circuit  by  the  sides  d  d,  to  re-enter, 
not  by  the  pole  <z,  but  by  the  pole  A,  of  the  other 
loadstone,  completing  the  circuit  by  e  f.  Thus  the 
vortices  of  these  two  loadstones  will  unite,  as  if  there 
were  but  one ;  and  this  vortex,  being  compressed  on 
all  sides  by  the  ether,  will  impel  the  two  loadstones 
towards  each  other,  so  that  they  will  exhibit  a  mutual 
attraction. 

This  is  the  reason  why  the  poles  of  different  names 
are  denominated/n'end/y,  and  those  of  the  same  name 
hostile,  the  principal  phenomenon  in  magnetism,  in 
as  much  as  the  poles  of  different  names  attract,  and 
those  of  the  same  name  repel  each  other. 

7th  November,  1761. 


LETTER  LXIV. 

Nature  of  Iron  and  Steel.     Method  of  communicating- 
to  them  the  Magnetic  Force. 

HAVING  settled  the  nature  of  the  loadstone  in  these 

canals  which  the  magnetic  matter  can  pervade  in 

only  one  direction,  because  the  valves  they  contain 

prevent  its  return  in  the  contrary  direction,  you  can 

T2 


222  METHOD    OF    COMMUNICATING 

no  longer  doubt  that  they  are  the  continuation  of 
those  pores  (see  Fig.  115,  p.  217),  whose  fibres 
point  in  the  same  direction ;  so  that  several  of  these 
particles,  being  joined  in  continuation,  constitute  one 
magnetic  canal.  It  is  not  sufficient,  therefore,  that 
the  matter  of  the  loadstone  should  contain  many 
similar  particles ;  they  must  likewise  be  disposed  in 
such  a  manner  as  to  form  canals  continued  from  one 
extremity  to  the  other,  in  order  to  grant  an  uninter- 
rupted transmission  to  the  magnetic  matter. 

Iron  and  steel,  then,  apparently  contain  such  par- 
ticles in  great  abundance ;  these  are  not,  however, 
originally  disposed  in  the  manner  I  have  been  de- 
scribing, but  are  scattered  over  the  whole  mass,  and 
this  disposition  is  all  they  want  to  become  real  mag- 
nets. In  that  case,  they  still  retain  all  their  other 
qualities,  and  are  not  distinguishable  from  other 
masses  of  iron  and  steel,  except  that  now  they  have 
besides  the  properties  of  the  loadstone ;  a  knife  and 
a  needle  answer  the  same  purposes,  whether  they 
have  or  want  the  magnetic  virtue.  The  change 
which  takes  place  in  the  interior,  from  the  arrange- 
ment of  the  particles  in  the  order  which  magnetism 
requires,  is  not  externally  perceptible  ;  and  the  iron 
or  steel  which  has  acquired  the  magnetic  force  is 
denominated  an  artificial  magnet,  to  distinguish  it 
from  the  natural,  which  resembles  a  stone,  though 
the  magnetic  properties  are  the  same  in  both:  You 
will  have  a  curiosity,  no  doubt,  to  be  informed  in 
what  manner  iron  and  steel  may  be  brought  to  re- 
ceive the  magnetic  force,  and  so  become  artificial 
magnets.  Nothing  can  be  more  simple;  and  the 
vicinity  of  a  loadstone  is  capable  of  rendering  iron 
somewhat  magnetic :  it  is  the  magnetic  vortex  which 
produces  this  effect,  even  though  the  iron  and  load- 
stone should  not  come  into  contact. 

However  hard  iron  may  appear,  the  particles  which 
contain  the  magnetic  pores  formerly  represented  are 
very  pliant  in  substance,  and  the  smallest  force  is 


THE    MAGNETIC   FORCE.  223 

sufficient  to  change  their  situation.  The  magnetic 
matter  of  the  vortex,  entering  into  the  iron,  will  then 
easily  dispose  the  first  magnetic  pores  which  it 
meets  following  its  own  directions — those  at  least 
whose  situation  is  not  very  different ;  and  having  run 
through  them,  it  will  act  in  the  same  manner  on  the 
adjacent  pores,  till  it  has  forced  a  passage  quite 
through  the  iron,  and  thereby  formed  some  magnetic 
canals.  The  figure  of  the  iron  contributes  greatly 
to  facilitate  this  change ;  a  lengthened  figure,  and 
placed  in  the  same  direction  with  the  vortex,  is  most 
adapted  to  it,  as  the  magnetic  matter,  in  passing 
through  the  whole  length,  disposes  there  a  great 
many  particles  in  their  just  situation,  in  order  to 
form  longer  magnetic  canals ;  and  it  is  certain,  that 
the  more  there  is  the  means  of  forming  canals,  and 
the  longer  they  are  without  interruption,  the  more 
rapid  will  be  the  motion  of  the  magnetic  matter,  and 
the  greater  the  magnetic  force. 

It  has  likewise  been  remarked,  that  when  the  iron 
placed  in  a  magnetic  vortex  is  violently  shaken  or 
struck,  it  acquires  a  higher  degree  of  magnetism 
from  this,  because  the  minute  particles  are  by  such 
concussion  agitated  and  disengaged,  so  as  to  yield 
more  easily  to  the  action  of  the  magnetic  matter 
which  penetrates  them. 

Placing  accordingly  a  small  Fig.  119. 

bar  of  iron  a  b,  Fig.  119,  in  the 
vortex  of  the  loadstone  A  B, 
so  that  its  direction  may  nearly 
agree  with  that  of  the  current 
d  cf  of  the  magnetic  matter,  it 
will  with  ease  pass  through 
the  bar,  and  form  in  it  mag- 
netic canals,  especially  if  at 
the  same  time  the  bar  is  sha- 
ken or  struck  to  facilitate  the 
transmission.  It  is  likewise 
observable,  that  the  magnetic  matter  which  enters 


224  METHOD    OF    COMMUNICATING 

at  the  pole  A  of  the  loadstone,  and  escapes  at  the 
pole  B,  will  enter  the  bar  at  the  extremity  a,  and 
escape  at  the  extremity  6,  so  that  the  extremity  a 
will  become  the  pole  of  the  same  name  A,  and  b  the 
same  with  B.  Then  taking  this  bar  a  b  out  of  the 
magnetic  vortex,  it  will  be  an  artificial  magnet, 
though  very  feeble,  which  will  supply  its  own  vor- 
tex, and  preserve  its  magnetic  power,  as  long  as  its 
magnetic  canals  shall  not  be  interrupted.  This  will 
take  place  so  much  the  more  easily  that  the  pores  of 
iron  are  pliant ;  thus  the  same  circumstance  which 
assists  the  production  of  magnetism  contributes 
likewise  to  its  destruction.  A  natural  magnet  is 
not  so  easily  enfeebled,  because  the  pores  are  much 
closer,  and  more  considerable  efforts  are  requisite  to 
derange  them.  1  shall  go  more  largely  into  the  de- 
tail afterward. 

I  here  propose  to  explain  ,the  manner  of  mbst 
naturally  rendering  iron  magnetic  ;  though  the  force 
which  it  thence  acquires  is  very  small,  it  will  assist 
us  in  comprehending  this  remarkable-  and  almost 
universal  phenomenon.  It  has  been  observed,  that 
tongs  and  other  implements  of  iron  which  are 
usually  placed  in  a  vertical  position,  as  well  as  bars 
of  iron  fixed  perpendicularly  on  steeples,  acquire  in 
time  a  very  sensible  magnetic  force.  It  has  likewise 
been  perceived  that  a  bar  of  iron,  hammered  in  a 
vertical  position  or  heated  red-hot,  on  being  plunged 
into  cold  water  in  the  same  position,  becomes  some- 
what magnetic,  without  the  application  of  any  load- 
stone. 

In  order  to  account  for  this  phenomenon,  you  have 
only  to  recollect  that  the  earth  itself  is  a  loadstone, 
and  consequently  encompassed  with  a  magnetic  vor- 
tex, of  which  the  declination  and  inclination  of  the 
magnetic  needle  everywhere  show  the  true  direction. 
If  then  a  bar  of  iron  remain  long  in  that  position, 
there  is  no  reason  to  be  surprised  should  it  become 
magnetic.  We  have  likewise  seen  that  the  inclina- 


THE    MAGNETIC    FORCE.  225 

/ 

tion  of  the  magnetic  needle  is  at  Berlin  72  degrees ; 
and  as  it  is  nearly  the  same  all  over  Europe,  this 
inclination  differs  only  18  degrees  from  the  vertical 
position;  the  vertical  position,  accordingly,  differs 
but  little  from  the  direction  of  the  magnetic  vortex : 
a  bar  of  iron,  long  kept  in  that  position,  will  be  at 
last  penetrated  with  the  magnetic  vortex,  and  must 
consequently  acquire  a  magnetic  force. 

In  other  countries,  where  the  inclination  is  im- 
perceptible, which  is  the  case  near  the  equator,  it  is 
not  the  vertical,  but  rather  the  horizontal  position, 
which  renders  bars  of  iron  magnetic ;  for  their  posi- 
tion must  correspond  to  the  magnetic  inclination,  if 
you  would  have  them  acquire  a  magnetic  force.  I 
speak  here  only  of  iron ;  steel  is  too  hard  for  the 
purpose,  and  means  more  efficacious  must  be  em- 
ployed to  communicate  the  magnetic  Virtue  to  it.* 

10£A  November,  1761. 

*  Captain  Scoresby  has  lately  discovered  a  method  of  making  artificial 
magnets,  solely  from  the  process  of  hammering  soft  steel  He  found  that 
a  bar  of  soft  steel,  6£  inches  long,  $  of  an  inch  in  diameter,  and  weighing 
392  grains,  when  hammered  in  a  vertical  direction,  on  a  surface  of  metal 
not  ferruginous,  acquired,  after  seventeen  blows,  a  lifting  power  of  6£ 
grains.  When  a  similar  bar  was  hammered,  with  its  lower  end  resting 
on  the  top  of  a  small  poker,  it  lifted  a  nail  of  88  grains  weight,  after 
twenty-two  blows.  When  the  poker  had  been  previously  hammered  in 
a  vertical  position,  a  single  blow  gave  the  bar  a  lifting  power  of  20  grains; 
and  in  one  instance  ten  blows  produced  a  lifting  power  of  188  grains. 
When  a  single  blow  was  struck  upon  the  bar  when  held  with  the  other 
end  up,  its  magnetism  was  almost  entirely  destroyed. 

These  curious  results  have  a  most  important  practical  application. 
Captain  Scoresby  has  shown  how  we  may  by  this  process  convert  the 
blade  of  a  penknife,  the  limb  of  a  pair  of  scissors,  or  even  a  nail,  into  a 
compass-needle,  which  will  traverse  with  great  facility  when  suspended 
by  a  hair  or  a  slender  thread.  By  this  means  the  shipwrecked  mariner 
may  guide  himself  in  his  boat  as  accurately  as  if  he  had  been  able  to  use 
his  compass.  For  further  infonnaiion  on  this  subject  see  the  Edinburgh 
Transactions,  vol.  ix.  p.  243  ;  Philosophical  Transactions,  1822,  p.  241  ; 
and  Edinburgh  Philosophical  Journal,  vol.  ix.  p.  41. — Ed. 


226    ACTION  OF  LOADSTONES  ON  IRON. 


LETTER  LXV. 

Action  of  Loadstones  on  Iron.     Phenomena  observable 
on  placing  Pieces  of  Iron  near  a  Loadstone. 

THOUGH  the  whole  earth  may  be  considered  as  a 
vast  loadstone,  and  as  encompassed  with  a  magnetic 
vortex  which  everywhere  directs  the  magnetic  nee- 
dle, its  magnetic  power  is,  however,  very  feeble,  and 
much  less  than  that  of  a  very  small  loadstone  :  this 
appears  very  strange,  considering  the  enormous 
magnitude  of  the  earth. 

It  arises  undoubtedly  from  our  very  remote  dis- 
tance from  the  real  magnetic  poles  of  the  earth, 
which,  from  every  appearance,  are  buried  at  a  great 
depth  below  the  surface :  now,  however  powerful  a 
loadstone  may  be,  its  force  Is  considerable  only 
when  it  is  very  near  ;  and  as  it  removes,  that  force 
gradually  diminishes,  and  at  length  disappears.  For 
this  reason  the  magnetic  force  acquired  in  time  by 
masses  of  iron  suitably  placed  in  the  earth's  vortex 
is  very  small,  and  indeed  hardly  perceptible,  unless 
it  is  very  soft,  and  of  a  figure  adapted  to  the  produc- 
tion of  a  vortex,  as  has  been  already  remarked. 

This  effect  is  much  more  considerable  near  a  load- 
stone of  moderate  size :  small  masses  of  iron  speedily 
acquire  from  it  a  very  perceptible  magnetic  force — 
they  are  likewise  attracted  towards  the  loadstone ; 
whereas  this  effect  is  imperceptible  in  the  earth's 
vortex,  and  consists  only  in  directing  magnetic 
needles,  without  either  attracting  them  or  increas- 
ing their  weight. 

A  mass  of  iron  plunged  into  the  vortex  of  a  load- 
stone likewise  presents  very  curious  phenomena, 
which  well  deserve  a  particular  explanation.  Not 
only  is  this  mass  at  first  attracted  towards  the  load- 
stone, butjt  too  attracts  other  pieces  of  iron.  Let 


ACTION  OF  LOADSTONES  ON  IRON. 


227 


A  B,  Fig.  120,  be  a  natural  magnet,  in  the  vicinity 
of  which,  at  the  pole  B,  is  placed  the  mass  of  iron 
C  D,  and  it  will  be  found  that  this  last  is  capable  of 


supporting  a  bar  of  iron  E  F.  Apply  again  to  this, 
at  F,  an  iron  ruler  G  H,  in  any  position  whatever,  say 
horizontal,  supporting  it  at  H,  and  it  will  be  found 
that  the  ruler  is  not  only  attracted  by  the  bar  F,  but 
likewise  capable  of  supporting  at  H  needles  as  I  K, 
and  that  these  needles  again  act  on  filings  of  iron 
L,  and  attract  them. 

The  magnetic  force  may  thus  be  propagated  to 
very  considerable  distances,  and  even  made  to  change 
its  direction,  by  the  different  position  of  these  pieces 
of  iron,  though  it  gradually  diminishes.  You  are 
perfectly  sensible,  that  the  more  powerful  the  load- 
stone A  B  is  of  itself,  and  the  nearer  to  it  the  first 
mass  C  D,  the  more  considerable  likewise  is  the 
effect.  The  late  Mr.  de  Maupertuis  had  a  large  load- 


228  ACTION    OF    LOADSTONES    ON    IRON. 

stone  so  powerful  that  at  the  distance  even  of  several 
feet,  the  mass  of  iron  C  D  continued  to  exert  a  very 
considerable  force. 

In  order  to  explain  these  phenomena,  you  have 
only  to  consider  that  the  magnetic  matter  which 
escapes  rapidly  at  the  pole  of  the  loadstone  B  enters 
into  the  mass  of  iron,  and  disposes  the  pores  of  it 
to  form  magnetic  canals,  which  it  afterward  freely 
pervades.  In  like  manner,  on  entering  into  the  bar, 
it  will  there  too  form  magnetic  canals — and  so  on. 
And  as  the  magnetic  matter,  on  issuing  from  one 
body,  enters  into  another,  these  two  bodies  must  un- 
dergo a  mutual  attraction,  for  the  same  reason,  as 
I  have  before  proved,  that  two  loadstones,  which 
present  their  friendly  poles  to  each  other,  must  be 
attracted ;  and  as  often  as  we  observe  an  attraction 
between  two  pieces  of  iron,  we*  may  with  certainty 
conclude  that  the  magnetic  matter  which  issues 
from  the  one  is  entering  into  the  other,  from  the 
continual  motion  with  which  it  penetrates  these 
bodies.  It  is  thus  that,  in  the  preceding  disposition 
of  the  |jars  of  iron,  the  magnetic  matter  in  its  motion 
pervades  all  of  them  ;  and  this  is  the  only  reason  of 
their  mutual  attraction. 

The  same  phenomena  still  present  themselves  on 
turning  the  other  pole  A  of  the  loadstone,  by  which 
the  magnetic  matter  enters,  towards  the  mass  of 
iron.  The  motion  in  this  case  becomes  retrograde, 
and  preserves  the  same  course ;  for  the  magnetic 
matter  contained  in  the  mass  of  iron  will  then  escape 
from  it,  to  pass  rapidly  into  the  loadstone,  and  in 
making  its  escape  will  employ  the  same  efforts  to 
arrange  the  pores  in  the  mass  suitably  to  the  current, 
as  if  it  were  rapidly  entering  into  the  iron.  To  this 
end,  therefore,  the  iron  must  be  sufficiently  soft  and 
these  pores  pliant  to  obey  the  efforts  of  the  magnetic 
matter.  A  difficulty  will  no  doubt  here  occur  to 
you ;  it  will  be  asked,  How  do  you  account  for  the 
change  of  direction  of  the  magnetic  matter  on  enter- 


ACTION   OF    LOADSTONES    ON   IRON. 


229 


ing  into  another  bar  of  iron ;  and  why  is  that  direc- 
tion regulated  according  to  the  length  of  the  bars, 
as  its  course  is  represented  in  the  figure  ?  This  is 
a  very  important  article  in  the  theory  of  magnetism, 
and  it  proves  how  much  the  figure  of  the  pieces 
of  iron  contributes  to  the  production  of  the  magnetic 
phenomena. 

To  elucidate  this,  it  must  be  recollected  that  this 
subtile  matter  moves  with  the  utmost  ease  in  the 
magnetic  pores,  where  it  is  separated  from  the  ether; 
and  that  it  encounters  very  considerable  obstacles 
when  it  escapes  from  them,  with  all  its  velocity,  to 
re-enter  into  the  ether  and  the  air. 

Let  us  suppose  that  the  magnetic  matter,  after 
having  pervaded  the  bar  C  D,  Fig.  121,  enters  into  the 
iron  ruler  E  F,  placed  per- 
pendicularly. It  would  cer-  Fig.  121. 

tainly,  on  its  first  admis-    3?  P  _  ^          c 

sion,  preserve  the  same  m  '• 
direction,  in  order  to  es- 
cape at  m,  unless  it  found 
an  easier  road  in  which  to 
continue  its  motion:  but 
meeting  at  m  the  great- 
est obstruction,  it  at  first 
changes  its  direction, 
though  in  a  very  small 
degree,  towards  F,  where 
finding  pores  adapted  to  r 
the  continuation  of  its  motion,  it  will  deviate  more 
and  more  from  its  first  direction,  and  travel  through 
the  ruler  E  F  in  all  its  length ;  and,  as  if  the  magnetic 
matter  were  loath  to  leave  the  iron,  it  endeavours  to 
continue  its  motion  there  as  long  as  possible,  avail- 
ing itself  of  the  length  of  the  ruler ;  but  if  the  ruler 
were  very  short,  it  would  undoubtedly  escape  at  m. 
But  the  length  of  the  ruler  presenting  it  a  space  to 
run  through,  it  follows  the  direction  E  F,  till  it  is 
under  the  necessity  of  escaping  at  F.  where  all  the 

VOL.  II.— U 


230  ARMING    OF    LOADSTONES. 

magnetic  canals,  formed  according  to  the  same 
direction,  no  longer  permit  the  subtile  magnetic 
matter  to  change  its  direction  and  return  along  the 
ruler ;  these  canals  being  not  only  filled  with  suc- 
ceeding matter,  but,  from  their  very  nature,  incapa- 
ble of  receiving  motion  in  an  opposite  direction. 
Uth  November,  1761. 


LETTER  LXVI. 

Arming  of  Loadstones. 

You  have  just  seen  how  iron  may  receive  the 
magnetic  current  of  a  loadstone,  convey  it  to  con- 
siderable distances,  and  even  change  its  direction. 
To  unite  a  loadstone,  therefore,  to  pieces  of  iron,  is 
much  the  same  with  increasing  its  size,  as  the  iron 
acquires  the  same  nature  with  respect  to  the  mag- 
netic matter ;  and  it  being  further  possible  by  such 
means  to  change  the  direction  of  the  magnetic  cur- 
rent, as  the  poles  are  the  places  where  this  matter 
enters  the  loadstone  and  escapes,  we  are  enabled  to 
conduct  the  poles  at  pleasure. 

On  this  principle  is  founded  the  arming,  or  mount- 
ing, of  loadstones — a  subject  well  worthy  of  your 
attention,  as  loadstones  are  thus  brought  to  a  higher 
degree  of  strength. 

Loadstones,  on  being  taken  from  the  mine,  are 
usually  reduced  to  the  figure  of  a  parallelepiped,  or 
rectangular  parallelogram,  with  thickness  as  A  A,  B  B, 
Fig.  122,  of  which  the  sur-  Fig.  122. 

face  A  A  is  the  pole  by  which 
the  magnetic  matter  enters, 
and  B  B  that  by  which  it  es- 
capes.  It  is  filled,  then,  the 
whole  length  A  B  with  canals 
a  b,  which  the  magnetic  mat- 
ter, impelled  by  the  elastic  power  of  the  ether,  freely 


ARMING   OF    LOADSTONES. 


231 


pervades  with  the  utmost  rapidity,  and  without  any 
mixture  of  that  fluid.  Let  us  now  see  in  what  manner 
such  a  loadstone  is  usually  armed. 

To  each  surface,  A  A 
and  B  B,  Fig.  123,  the  two 
poles  of  the  loadstone,  are 
applied  plates  of  iron  a  a 
and  b  b,  terminating  below 
in  the  knobs  A'  and  B'  call- 
ed the  feet  ;  this  is  what 
we  denominate  the  ar- 
mour  of  the  loadstone,  and 
when  this  is  done,  the 
loadstone  is  said  to  be 
armed.  In  this  state,  the 
magnetic  matter  which  would  have  escaped  at  the 
surface  B  B  passes  into  the  iron  plate  b  b1  where  the 
difficulty  of  flying  off  into  the  air,  in  its  own  direc- 
tion, obliges  it  to  take  a  different  one,  and  to  flow 
along  the  plate  b  b  into  the  foot  B',  and  there  it  is 
under  the  necessity  of  escaping,  as  it  no  longer  finds. 
iron  to  assist  the  continuation  of  its  motion.  The 
same  thing  takes  place  on  the  other  side  ;  the  subtile 
matter  will  be  there  conducted  through  the  foot  A', 
from  which  it  will  pass  into  the  plate  a  a,  changing 
its  direction  to  enter  into  the  loadstone,  and  to  fly 
through  its  magnetic  canals.  For  the  subtile  matter 
contained  in  the  plate  enters  first  into  the  load- 
stone ;  it  is  followed  by  that  which  is  the  foot  A', 
replaced  in  its  turn  by  the  external  magnetic  matter, 
which,  being  there  impelled  by  the  elasticity  of  the 
ether,  penetrates  the  foot  A'  and  the  plate  a  a  with  a 
rapidity  whose  vehemence  is  capable  of  arranging 
the  poles,  and  of  forming  magnetic  canals. 

Hence  it  is  evident  that  the  motion  must  be  the 
same  on  both  sides,  with  this  difference,  that  the 
magnetic  matter  will  enter  by  the  foot  A',  and  es- 
cape by  the  foot  B',  so  that  in  these  two  feet  we 
now  find  the  poles  of  the  armed  loadstone  ;  and  as 


232  ARMING    OF   LOADSTONES. 

the  poles  formerly  diffused  over  the  surfaces  A  A 
and  B  B  are  now  collected  on  the  basis  of  the  feet 
A'  and  B',  it  is  naturally  to  be  supposed  that  the  mag- 
netic force  must  be  considerably  greater  in  these 
new  poles. 

In  this  state,  accordingly,  the  vortex  will  be  more 
easily  formed.  The  matter  escaping  from  the  foot 
B'  will,  with  the  utmost  facility,  return  to  the  foot 
A',  passing  through  C ;  and  the  rest  of  the  body  of 
the  loadstone  will  not  be  encompassed  by  any  vor- 
tex, unless  perhaps  a  small  quantity  of  magnetic 
matter  should  escape  from  the  plate  b  b,  from  its 
not  being  able  to  change  the  direction  so  suddenly ; 
and  unless  a  small  quantity  should  find  admission 
by  the  plate  a  a,  which  in  that  case  might  produce 
a  feeble  vortex,  whereby  the  subtile  matter  would 
be  immediately  conducted  from  the  plate  b  b  to  a  a  ; 
however,  if  the  armour  be  well  fitted,  this  second 
vortex  will  be  almost  imperceptible,  and  conse- 
quently the  current  between  the  feet  is  so  much  the 
stronger. 

The  principal  direction  for  arming  loadstones  is 
carefully  to  polish  both  surfaces  of  the  loadstone 
A  A  and  B  B,  as  well  as  the  plates  of  iron,  so  that  on 
applying  them  to  the  loadstone,  they  may  exactly 
touch  it  in  every  point,  the  subtile  matter  passing 
easily  from  the  loadstone  to  the  iron,  when  unob- 
structed by  any  intervening  matter ;  but  if  there  be 
a  vacuum,  or  a  body  of  air,  between  the  loadstone 
and  the  plates,  the  magnetic  matter  will  lose  almost 
all  its  motion,  its  current  will  be  interrupted,  and 
rendered  incapable  of  forcing  its  passage  through 
the  iron,  by  forming  magnetic  canals  in  it. 

The  softest  and  most  ductile  iron  is  to  be  preferred 
,br  the  construction  of  such  armour,  because  its 
,x>res  are  pliant,  and  easily  arrange  themselves  in 
conformity  to  the  current  of  the  magnetic  matter. 
Iron  of  this  description,  accordingly,  appears  well 
adapted  to  the  production  of  a  sudden  change  in 


ARMING    OF   LOADSTONES.  233 

the  direction  of  the  current :  the  magnetic  matter, 
too,  seems  to  affect  a  progress  in  that  direction  as 
long  as  possible,  and  does  not  quit  it  till  the  continu- 
ance of  its  motion  through  that  medium  is  no  longer 
practicable:  it  prefers  making  a  circuit  to  a  pre- 
mature departure — a  thing  that  does  not  take  place 
in  the  loadstone  itself,  in  which  the  magnetic  canals 
are  already  formed,  nor  in  steel,  whose  pores  do  not 
so  easily  yield  to  the  efforts  of  a  magnetic  current. 
But  when  these  canals  are  once  formed  in  steel, 
they  are  not  so  easily  deranged,  and  much  longer 
retain  their  magnetic  force ;  whereas  soft  iron, 
whatever  force  it  may  have  exerted  during  its  junc- 
tion with  a  loadstone,  loses  it  almost  entirely  on 
being  disjoined. 

Experience  must  be  consulted  as  to  the  other  cir- 
cumstances of  arming  loadstones.  Respecting  the 
plates,  it  has  been  found  that  a  thickness  either  too 
great  or  too  small  is  injurious  ;  but  for  the  most  part, 
the  best  adapted  plates  are  very  thin,  which  would 
appear  strange,  did  we  not  know  that  the  magnetic 
matter  is  much  more  subtile  than  ether,  and  that 
consequently  the  thinnest  plate  is  sufficient  to  re- 
ceive a  very  great  quantity  of  it. 

nth  November,  1761. 

U2 


234 


ACTION   AND   FORCE    OF 


Pig.  124. 


p;- 

A 

'      B 
B 

J                        "    \_ 

LETTER  LXVn. 

Action  and  Force  of  armed  Loadstones. 

AT  the  feet  of  its  armour,  then,  a  loadstone  exerts 
its  greatest  force,  because  there  its  poles  are  col- 
lected ;  and  each  foot  is  capable  of  supporting  a  weight 
of  iron,  greater  or  less  in  proportion  to  the  excel- 
lence of  the  loadstone. 

Thus  a  loadstone  A  A,  B  B, 
Fig.  124,  armed  with  plates  of 
iron  a  a  and  b  b,  terminating  in 
the  feet  A'  and  B',  will  support 
by  the  foot  A'  not  only  the 
iron  ruler  C  D,  but  this  last 
will  support  another  of  small- 
er size  E  F,  this  again  another 
still  smaller  G  H,  which  will 
in  its  turn  support  a  needle 
I  K,  which,  finally,  will  at- 
tract filings  of  iron  L;  be- 
cause the  magnetic  matter 
runs  through  all  these  pieces 
to  enter  at  the  pole  A' ;  or  if  it 
were  the  other  pole  by  which 
the  magnetic  matter  issues 
from  the  loadstone,  it  would 
in  like  manner  run  through 
the  pieces  CD,EF,GH,  IK. 
Now,  as  often  as  the  matter 
is  transmitted  from  one  piece 
to  another,  an  attraction  be- 
tween the  two  pieces  is  ob- 
servable ;  or  rather  they  are  impelled  towards  each 
other  by  the  surrounding  ether,  because  the  current 
of  the  magnetic  matter  between  them  diminishes  the 
pressure  of  that  fluid. 


ARMED    LOADSTONES. 


235 


When  one  of  the  poles  of  the  loadstone  is  thus 
loaded,  its  vortex  undergoes  a  very  remarkable 
change  of  direction ;  for  as,  without  this  weight,  the 
magnetic  matter  which  issues  from  the  pole  B',  di- 
recting around  its  course,  would  flow  towards  the 
other  pole  A' ;  and  as  now  the  entrance  into  this 
pole  is  sufficiently  supplied  by  the  pieces  which  it 
supports,  the  matter  issuing  from  the  pole  B'  must 
take  quite  a  different  road,  which  will  at  length  con- 
duct it  to  the  last  piece  IK.  A  portion  of  it  will  un- 
doubtedly be  likewise  conveyed  towards  the  last  but 
one  G  H,  and  towards  those  which  precede  it ;  as 
those  which  follow,  being  smaller,  do  not  supply  in 
sufficient  abundance  those  which  go  before :  but  the 
vortex  will  always  be  extended  to  the  last  piece.  By 
these  means,  if  the  pieces  are  well  proportioned  to 
each  other  in  length  and  thickness,  the  loadstone  is 
capable  of  supporting  much  more  than  if  it  were 
loaded  with  a  single  piece,  in  which  the  figure  like- 
wise enters  principally  into  consideration.  But  in 
order  to  make  it  sustain  the  greatest  possible  weight, 
we  must  contrive  to  unite  the  force  of  both  poles. 

For  this  purpose,  there  is  applied  to  the  two  poles 


A.  and  B,  Fig.  127,  a 
piece  of  soft  iron  C  D, 
touching  the  base  of  the 
feet  in  all  points,  and 
whose  figure  is  such, 
that  the  magnetic  mat- 
ter which  issues  from 
B  shall  find  it  in  the 
most  commodious  pas- 
sage to  re-enter  at  the 
other  extremity  A. — 
Such  a  piece  of  iron  is 
called  the  supporter  of 
the  loadstone;  and  as 
the  magnetic  matter  en- 
ters into  it  on  issuing 


Fig.  127. 


^                             I 

t 

a 

1              m 

236  ACTION   AND    FORCE    OF 

from  the  loadstone  at  B,  and  enters  into  the  other 
pole  A,  on  issuing  from  the  supporter,  the  iron  will 
be  attracted  at  both  poles  at  once,  and  consequently 
adhere  to  them  with  great  force.  In  order  to  know 
how  much  power  the  loadstone  exerts,  there  is  affixed 
to  the  supporter,  at  the  middle  E,  a  weight  P,  which 
is  increased  till  the  loadstone  is  no  longer  capable  of 
sustaining  it ;  and  then  that  weight  is  said  to  coun- 
terbalance the  magnetic  power  of  the  loadstone :  this 
is  what  you  are  to  understand  when  told  that  such 
a  loadstone  carries  ten  pounds  weight,  such  another 
thirty,  and  so  on.  Mahomet's  coffin,  they  pretend, 
is  supported  by  the  force  of  a  loadstone — a  thing  by 
no  means  impossible,  as  artificial  magnets  have 
already  been  constructed  which  carry  more  than  100 
pounds  weight. 

A  loadstone  armed  with  its  suppprter  loses  nothing 
of  the  magnetic  matter,  which  performs  its  complete 
vortex  within  the  loadstone  and  the  iron,  so  that 
none  of  it  escapes  into  the  air.  Since  then  mag- 
netism exerts  its  power  only  in  so  far  as  the  matter 
escapes  from  one  body  to  enter  into  another,  a  load- 
stone whose  vortex  is  shut  up  should  nowhere  exert 
the  magnetic  power ;  nevertheless,  when  it  is  touched 
on  the  plate  at  a  with  the  point  of  a  needle,  a  very 
powerful  attraction  is  perceptible,  because  the  mag- 
netic matter,  being  obliged  suddenly  to  change  its 
direction,  in  order  to  enter  into  the  canals  of  the 
loadstone,  finds  a  more  commodious  passage  by 
running  through  the  needle,  which  will  consequently 
be  attracted  to  the  plate  a  a.  But  by  that  very  thing 
the  vortex  will  be  deranged  inwardly ;  it  will  not 
flow  so  copiously  into  the  feet ;  and  if  you  were  to 
apply  several  needles  to  the  plate,  or  iron  rulers  still 
more  powerful,  the  current  towards  the  feet  would 
be  entirely  diverted,  and  the  force  which  attracts  the 
supporter  would  altogether  disappear,  so  that  it 
would  drop  off  without  effort.  Hence  it  is  evident 
that  the  feet  lose  their  magnetic  power  in  proportion 


ARMED   LOADSTONES.  237 

as  the  loadstone  exercises  its  force  in  other  places ; 
and  thus  we  are  enabled  to  account  for  a  variety  of 
very  surprising  phenomena,  which  without  the  the- 
ory, would  be  absolutely  inexplicable. 

This  is  the  proper  place  for  introducing  the  experi- 
ment which  demonstrates,  that  after  having  applied 
its  supporter  to  an  armed  loadstone,  you  may  go  on 
from  day  to  day  increasing  the  weight  which  it  is 
able  to  sustain,  till  it  at  length  shall  exceed  the 
double  of  what  it  carried  at  first.  It  is  necessary  to 
show,  therefore,  how  the  magnetic  force  may  in 
time  be  increased  in  the  feet  of  the  armour.  The 
case  above  described,  of  the  derangement  of  the 
vortex,  assures  us,  that  at  the  moment  when  the 
supporter  is  applied,  the  current  of  the  magnetic 
matter  is  still  abundantly  irregular,  that  a  consider- 
able part  of  it  is  still  escaping  by  the  plate  b  i,  and 
that  it  will  require  time  to  form  magnetic  canals  in 
the  iron  :  it  is  likewise  probable  that,  when  the  cur- 
rent shall  have  become  more  free,  new  canals  may- 
be formed  in  the  loadstone  itself,  considering  that  it 
contains,  besides  these  fixed  canals,  moveable  poles, 
as  iron  does.  But  on  violently  separating  the  sup- 
porter from  the  loadstone,  the  current  being  dis- 
turbed, and  these  new  canals  in  a  great  measure 
destroyed,  the  force  is  suddenly  rendered  as  small 
as  at  the  beginning ;  and  some  time  must  intervene 
before  these  canals,  with  the  vortex,  can  recover 
their  preceding  state.  I  once  constructed  an  arti- 
ficial magnet,  which  at  first  could  support  only  ten 
pounds  weight;  and  after  some  time  I  was  sur- 
prised to  find  that  it  could  support  more  than  thirty. 
It  is  remarked,  chiefly  in  artificial  magnets,  that  time 
alone  strengthens  them  considerably ;  but  that  this 
increase  of  force  lasts  only  till  the  supporter  is  sepa- 
rated from  it. 

21st  November,  1761. 


238  METHOD   OF    COMMUNICATING 


LETTER  LXVIII. 

The  Method  of  communicating  to  Steel  the  Magnetic 
Force,  and  of  magnetizing  Needles  for  the  Compass: 
the  Simple  Touch,  its  Defects  ;  Means  of  remedying 
these. 

HAVING  explained  the  nature  of  magnets  in  general, 
an  article  as  curious  as  interesting  still  remains  ; 
namely,  the  manner  of  communicating  to  iron,  but 
especially  to  steel,  the  magnetic  power,  and  even 
the  highest  degree  possible  of  that  power. 

You  have  seen  that,  by  placing  iron  in  the  vortex 
of  a  loadstone,  it  acquires  a  magnetic  force,  but  which 
almost  totally  disappears  as  soon  as  it  is  removed 
out  of  the  vortex  ;  and  that  the  Cortex  of  the  earth 
alone  is  capable,  in  time,  of  impressing  a  slight  mag- 
netic power  upon  iron  ;  now,  steel  being  harder  than 
iron,  and  almost  entirely  insensible  to  this  action  of 
the  magnetic  vortex,  more  powerful  operations  must 
be  employed  to  magnetize  it  ;  but  then  it  retains  the 
magnetic  force  much  longer. 

For  this  purpose  we  must  have  recourse  to  touch- 
ing, and  even  to  friction.  I  begin,  therefore,  with 
explaining  the  method  formerly  employed  for  mag- 
netizing the  needles  of  compasses  ;  the  whole  opera- 
tion consisted  in  rubbing  them  at  the  pole  with  a 
good  loadstone,  whether  naked  or  armed. 

The  needle  a  b  c,  Fig.  125,  p^  135 

was  laid  on  a  table  ;  the  pole  nB  ** 

B  of  the  loadstone  was  drawn  IJ 


it,  from  b  towards  a,  and,  c 

being  arrived  at  the  extremity 

a,  the  loadstone  was  raised  aloft,  and  brought  back 
through  the  air  to  b  ;  this  operation  was  repeated 
several  times  together,  particular  care  being  taken 
that^he  other  pole  of  the  loadstone  should  not  come 


THE    MAGNETIC   FORCE.  239 

near  the  needle,  as  this  would  have  disturbed  the 
whole  process.  Having  several  times  drawn  the 
pole  B  of  the  loadstone  over  the  needle,  from  b  to  a, 
the  needle  had  become  magnetic,  and  the  extremity 
b  of  the  same  name  with  that  of  the  loadstone  with 
which  it  had  been  rubbed.  In  order  to  render  the 
extremity  b  the  north  pole,  it  would  have  been 
necessary  to  rub  with  the  pole  of  this  name  in 
the  loadstone,  proceeding  from  b  to  a ;  but  in  rub- 
bing with  the  south  pole,  the  progress  must  be  from 
a  to  b. 

This  method  of  rubbing,  or  touching,  is  denomi- 
nated the  simple  touch,  because  the  operation  is  per- 
formed by  touching  with  one  pole  only;  but  it  is 
extremely  defective,  and  communicates  but  very  little 
power  to  the  needle,  let  the  loadstone  be  ever  so 
excellent ;  accordingly,  it  does  not  succeed  when  the 
steel  is  carried  to  the  highest  degree  of  hardness, 
though  this  be  the  state  best  adapted  to  the  retention 
of  magnetism.  You  will  yourself  readily  discern  the 
defects  of  this  method  by  the  simple  touch. 

Let  us  suppose  that  B  is  the  pole  of  the  loadstone 
from  which  the  magnetic  matter  issues,  as  the  effect 
of  the  two  poles  is  so  similar  that  it  is  impossible  to 
perceive  the  slightest  difference ;  having  rested  the 
pole  on  the  extremity  b  of  the  needle,  the  magnetic 
matter  enters  into  it  with  all  the  rapidity  with  which 
it  moves  in  the  loadstone,  incomparably  greater  than 
that  of  the  vortex  which  is  in  the  external  air.  But 
what  will  become  of  this  matter  in  the  needle  ?  It 
cannot  get  out  at  the  extremity  £,  it  will  therefore 
make  an  effort  to  force  its  way  through  the  needle 
towards  <z,  and  the  pole  B,  moving  in  the  same  direc- 
tion, will  assist  this  effort ;  but  as  soon  as  the  pole 
B  shall  arrive  at  a,  the  difficulty  of  escaping  at  the 
extremity  a  will  occasion  a  contrary  effort,  by  which 
the  magnetic  matter  will  be  impelled  from  a  towards 
b ;  and  before  the  first  effect  is  entirely  destroyed 
this  last  cannot  take  place.  Afterward,  when  the 


240  MAGNETIC   FORCE. 

pole  B  is  again  brought  back  to  the  extremity  £,  this 
last  effect  is  again  destroyed,  but  without  producing, 
however,  a  current  in  the  contrary  direction  from  b 
towards  a  \  and  consequently,  when  the  pole  B  shall 
have  got  beyond  c  in  its  progress  towards  a,  it  will 
more  easily  produce  a  current  from  a  to  b,  especially 
if  you  press  more  hard  on  the  half  c  a :  hence  it  is 
clear,  that  the  needle  can  have  acquired  only  a  small 
degree  of  the  magnetic  power. 

Some,  accordingly,  rub  only  the  half  c  a  (Fig.  125, 
p.  238),  proceeding  from  c  to  a,  and  others  touch 
only  the  extremity  a  of  the  needle  with  the  pole  B 
of  the  loadstone,  and  with  nearly  the  same  success. 
But  it  is  evident  that  the  magnetic  matter  which 
enters  by  the  extremity  a  only  is  incapable  of  acting 
with  sufficient  vigour  on  the  pores  of  the  needle,  for 
arranging  them  conformably  to*  the  laws  of  mag- 
netism ;  and  that  the  force  impressed  by  this  method 
must  be  extremely  small,  if  any  thing,  when  the  steel 
is  very  much  hardened. 

Tt  appears  to  me,  then,  that  these  defects  of  the 
simple  touch  might  be  remedied  in  the  following 
manner ;  of  the  success  of  which  I  entertain  no 
doubt,  though  I  have  not  yet  tried  it ;  but  am  con- 
firmed in  my  opinion  by  experiments  which  I  have 
made. 

I  would  case  the  extremity  b  of  the  needle,  Fig. 
126,  in  a  ruler  of  soft  iron  E  F;  p-  126 

and  I  should  think  it  proper  to 

make  that  ruler  very  thin,  and  as  dfcqfi   MB  _g | 

straight  as  possible  ;  but  the  ex- 
tremity must  be  exactly  applied  in  all  points,  and 
even  fitted  to  a  groove  perfectly  adjusted  for  its  re- 
ception. On  resting  the  pole  B  of  the  loadstone  upon 
the  extremity  b  of  the  needle,  the  magnetic  matter 
which  enters  into  it,  meeting  scarcely  any  difficulty 
in  its  progress  through  the  iron  ruler,  will  at  once 
pursue  its  course  in  the  direction  b  d ;  and  in  pro- 
portion as  the  pole  advances  towards  «,  the  mag- 


OF  PRESERVING  MAGNETIC  MATTER.    241 

netic  matter,  in  order  to  continue  this  course,  has 
only  to  arrange  the  pores  on  which  it  immediately 
acts;  and  having  reached  a,  all  these  pores,  or  at 
least  by  far  the  greater  number  of  them,  will  be 
already  disposed  conformably  to  that  direction. 
When  you  afterward  recommence  the  friction  at 
the  extremity  6,  nothing  is  destroyed ;  but  you  con- 
tinue to  perfect  the  current  of  the  magnetic  matter, 
following  the  same  direction  b  d,  by  likewise  arran- 
ging the  pores  which  resisted  the  first  operation ;  and 
thus  the  magnetic  canals  in  the  needle  will  always 
become  more  perfect.  A  few  strokes  of  the  pole  B 
will  be  sufficient  for  the  purpose,  provided  the  load- 
stone is  not  too  weak  ;  and  I  have  no  doubt  that  the 
best  tempered  steel,  that  is,  rendered  as  hard  as  pos- 
sible, would  yield  to  this  method  of  operating;  an 
unspeakable  advantage  in  the  construction  of  com- 
passes, as  it  has  been  found  that  ordinary  needles 
frequently  lose,  by  a  slight  accident,  all  their  mag- 
netic power ;  by  which  ships  at  sea  would  be  ex- 
posed to  the  greatest  dangers,  if  they  had  not  others 
in  reserve.  But  when  needles  are  made  of  well 
tempered  steel,  accidents  of  this  kind  are  not  so 
much  to  be  apprehended ;  for  if  a  greater  force  is 
requisite  to  render  them  magnetic,  in  return  they 
preserve  the  power  more  tenaciously. 
24th  November,  1761. 


LETTER  LXIX. 

On  the  Double  Touch.     Means  of  preserving  the 
netic  matter  in  Magnetized  Bars. 

INSTEAD  of  this  method  of  magnetizing  iron  or 
steel  by  the  simple  touch,  by  rubbing  with  one  pole 
only  of  the  loadstone,  we  now  employ  the  double 
touch,  in  which  we  rub  with  both  poles  at  once, 

VOL.  II.— X 


242 


MEANS    OF    PRESERVING 


which  is  easily  done  by  means  of  an  armed  load- 
stone. 


Fig.  130. 


j.  A 

B 

Let  E  F,  Fig.  130,  be  a 
bar  of  iron  or  steel,  which 
you  wish  to  render  mag- 
netic. Having  fixed  "it 
steadily  on  a  table,  you 
press  upon  it  the  two  feet 
A  and  B  of  an  armed  load- 
stone. In  this  state,  you  will  easily  see  that  the 
magnetic  matter  which  issues  from  the  loadstone  by 
the  foot  B  must  penetrate  into  the  bar,  and  would 
diffuse  itself  in  all  directions,  did  not  the  foot  A,  on 
its  side,  attract  the  magnetic  matter  contained  in  the 
pores  of  the  bar.  This  evacuation  therefore  at  d 
will  determine  the  matter  which  enters  by  the  pole 
B  to  take  its  course  from  c  towards  d,  provided  the 
poles  A  and  B  are  not  too  remote  from  each  other. 
Then  the  magnetic  current  will  force  its  way  in  the 
bar,  in  order  to  pass  from  the  pole  B  to  the  pole  A, 
disposing  its  pores  to  form  magnetic  canals  ;  and  it 
is  very  easy  to  discover  whether  this  is  taking  place  ; 
you  have  only  to  observe  if  the  loadstone  is  power- 
fully attracted  to  the  bar,  which  never  fails  if  the 
bar  is  of  soft  iron,  as  the  magnetic  matter  easily 
penetrates  it.  But  if  the  bar  is  of  steel,  the  attraction 
is  frequently  very  small — a  proof  that  the  magnetic 
matter  is  incapable  of  opening  for  itself  a  passage 
from  c  to  d ;  hence  it  is  to  be  concluded  that  the 


loadstone  is  too  feeble,  or  that  the 
distance  between  its  two  poles  is 
too  great :  in  this  case  it  would  be 
necessary  to  employ  a  loadstone 
more  powerful,  or  whose  feet  are 
nearer ;  or  finally,  the  armour  of 
the  loadstone  ought  to  be  changed 
into  the  form  reoresented  in  Fig. 
129. 


Fig.  129. 


THE  MAGNETIC  MATTER.         243 

But  the  following  is  a  method  of  remedying  "this 
inconvenience. 

Having  fixed  the  bar  as  in  c  d.  Fig.  130  (p.  242), 
the  loadstone  must  be  several  times  drawn  back- 
ward and  forward  over  it,  from  one  extremity  to  the 
other,  without  taking  it  off  till  you  perceive  that 
the  attraction  no  longer  increases ;  for  it  is  undoubt- 
edly certain  that  attraction  is  increased  in  propor- 
tion to  the  increase  of  the  magnetic  force.  The  bar 
E  F  will  be  magnetized  by  this  operation  in  such  a 
manner  that  the  extremity  E,  towards  which  the 
pole  A  was  turned,  will  be  the  friendly  pole  of  A, 
and  consequently  of  the  same  name  with  the  other 
pole  B.  Again,  on  removing  the  loadstone,  as  mag- 
netic canals  are  formed  the  whole  length  of  the  bar, 
the  magnetic  matter  diffused  through  the  air  will 
force  a  passage  through  these  canals,  and  will  make 
the  bar  a  real  magnet.  It  will  enter  by  the  extremity 
a,  and  escape  by  the  extremity  b,  from  whence  a 
part,  at  least,  will  return  to  a,  and  will  form  a  vor- 
tex such  as  the  nature  of  the  bar  permits. 

I  take  this  occasion  to  remark,  that  the  formation 
of  a  vortex  is  absolutely  necessary  to  the  increase 
of  magnetism :  for  if  all  the  magnetic  matter  which 
goes  out  at  the  extremity  b  were  to  fly  off,  and  be 
entirely  dispersed,  without  returning  to  a,  the  air 
would  not  supply  a  sufficient  quantity  to  the  other 
extremity  «,  which  must  occasion  a  diminution  of 
the  magnetic  force.  But  if  a  considerable  part  of 
that  which  escapes  at  the  extremity  b  returns  to  a, 
the  air  is  abundantly  able  to  supply  the  remainder, 
and  perhaps  still  more,  if  the  magnetic  canals  of  the 
bar  are  capable  of  receiving  it ;  the  bar  will  there- 
fore in  that  case  acquire  a  much  greater  magnetic 
force. 

This  consideration  leads  me  to  explain  how  it  is 
possible  to  keep  up  the  magnetic  matter  in  magnet- 
ized bars.  The  object  being  to  prevent  the  magnetic 
matter  which  pervades  them  from  dispersing  in  the 


244 


MEANS    OF   PRESERVING 


Pig.  131. 


air,  these  bars  are  always  disposed  in  pairs  of  ex- 
actly the  same  size.  They  are  placed  on  a  table,  in 
a  parallel  situation,  so  that  the  friendly  poles,  or 
those  of  different  names,  should  be  turned  to  the 
same  side  as  in  Fig.  131, 
where  M  M  and  N  N  rep- 
resent the  two  bars, 
whose  friendly  poles  a, 
6,  6,  a,  are  turned  the 
same  way.  To  prevent 
mistake,  a  mark  x  is 
made  on  each  bar,  at  the 
extremity  where  the 


north  pole  is,  and  to 
both  ends  is  applied  a 
piece  of  soft  iron  E  E 
and  F  F,  for  receiving-  the  magnetic  current. 


In 


this  manner,  the  whole  magnetic  matter  which  per- 
vades the  bar  M  M,  and  which  issues  at  the  extremity 
J,  passes  into  the  piece  of  iron  E  E,  where  it  easily 
makes  its  way,  to  enter  at  the  extremity  a  of  the 
other  bar  N  N,  from  which  it  will  escape  at  the  ex- 
tremity b,  into  the  other  piece  of  iron  F  F,  which 
reconveys  it  into  the  first  bar  M  M  by  the  extremity 
a.  Thus  the  magnetic  matter  will  continue  to 
circulate,  and  no  part  of  it  escape;  and  even  in 
case  there  should  not  be  at  first  a  sufficient  quantity 
to  supply  the  vortex,  the  air  will  supply  the  deficiency, 
and  the  vortex  will  preserve  all  its  force  in  the  two 
bars. 

This  disposition  of  the  two  bars  may  likewise  be 
employed  for  magnetizing  both  of  them  at  once. 
The  two  poles  of  a  loadstone  must  be  drawn  over 
the  two  bars,  passing  from  the  one  to  the  other  by 
,the  pieces  of  iron ;  and  the  circuit  must  be  several 
times  performed,  carefully  observing  that  the  two 
poles  of  the  loadstone  A  and  B  be  turned  as  the 
figure  directs. 

This  method  of  magnetizing  two  bars  at  once 


THE  MAGNETIC  MATTER.         245 

must  be  much  more  efficacious  than  the  preceding1, 
as  from  the  very  first  circuit  performed  by  the  load- 
stone, the  magnetic  matter  will  begin  to  flow 
through  the  two  bars  by  means  of  the  two  pieces  of 
iron.  Afterward,  by  repeated  circuitous  applications 
of  the  loadstone  to  the  bars,  a  greater  quantity  of 
pores  will  be  arranged  in  them  conformably  to  mag- 
netism, and  more  magnetic  canals  will  be  opened,  by 
which  the  vortex  will  be  more  and  more  strengthened, 
without  undergoing  any  diminution.  If  the  bars  are 
thick,  it  would  be  proper  to  turn  and  rub  them  in  the 
same  manner  on  the  other  surfaces,  in  order  that  the 
magnetic  action  may  penetrate  them  thoroughly. 

Having  obtained  these  magnetic  bars  M  M,  N  N, 
Fig.  132,  they  may  be  em-  Fig.  132. 

ployed  in  place  of  the  natu- 
ral loadstone,  for  magnet- 
izing   others.'    They    are 
joined  together  at  the  top, 
so  that  the  two  friendly  poles 
ab  may  touch  each  other; 
and    the  other   two    poles 
below,  b  and  a,  are   sepa- 
rated as  far  as  it  is  thought 
proper.     Then  we  rub  with  the  two  under  extremi 
ties,  which  supply  the  place  of  the  two  poles  of  a 
loadstone,  two  other  bars  E  F,  in  the  manner  which 
I  have  above  explained. 

As  these  two  bars  are  joined  in  the  form  of  com 
passes,  we  have  the  advantage  of  opening  the  lower 
extremities  as  much  or  as  little  as  we  please,  which 
cannot  be  done  with  a  loadstone  ;  and  the  magnetic 
current  will  easily  pass  at  top,  where  the  bars  touch 
each  other,  from  the  one  to  the  other.  A  small 
piece  of  soft  iron  P  might  likewise  be  applied  there, 
the  better  to  keep  up  the  current ;  and  in  this  man- 
ner you  may  easily  and  speedily  magnetize  as  many 
double  bars  as  you  please. 
November,  1761. 

X2 


246     MAGNETIC  FORCE  COMMUNICATED 


LETTER  LXX. 

The  Method  of  communicating  to  Bars  of  Steel  a 
very  great  magnetic  Force,  by  means  of  other  Bars 
which  have  it  in  a  very  inferior  degree. 

THOUGH  this  method  of  magnetizing  by  the  double 
touch  be  preferable  to  the  preceding,  the  magnetic 
power,  however,  cannot  be  carried  beyond  a  certain 
degree.  Whether  we  employ  a  natural  loadstone 
or  two  magnetic  bars  for  rubbing  other  bars,  these 
last  will  never  acquire  so  much  force  as  the  first ;  it 
being  impossible  that  the  effect  should  be  greater 
than  the  cause. 

If  the  bars  with  which  we  rub  have  little  force, 
those  which  are  rubbed  will  have  still  less :  the  rea- 
son is  evident;  for  as  bars  destitute  of  magnetic 
force  never  could  produce  it  in  others,  so  a  moderate 
degree  of  force  is  incapable  of  producing  one 
greater  than  itself,  at  least  by  the  method  which 
I  have  been  describing. 

But  this  rule  is  not  to  be  taken  in  the  strict  inter- 
pretation of  the  words,  as  if  it  were  literally  impos- 
sible to  produce  a  greater  magnetic  force  by  the 
assistance  of  a  smaller.  I  am  going  to  point  out  a 
method  by  which  the  magnetic  power  may  be  in- 
creased almost  as  far  as  you  please,  beginning  with 
the  smallest  degree  possible.  This  is  a  late  discov- 
ery, which  merits  so  much  the  more  attention  that 
it  throws  much  light  on  a  very  difficult  subject — 
the  nature  of  magnetism. 

Supposing  that  I  am  possessed  of  a  very  feeble 
loadstone,  or,  for  want  of  a  natural  magnet,  of  bars 
of  iron  rendered  somewhat  magnetic  merely  by  the 
vortex  of  the  earth,  as  I  explained  it  in  a  preceding 
Letter,  I  then  provide  myself  with  eight  bars  of  steel, 
very  small,  and  not  hardened,  in  order  the  more 
easily  to  receive  the  small  degree  of  magnetic  power 
which  the  feeble  loadstone,  or  slightly  magnetized 


TO    BARS    OF    STEEL.  247 

bars,  are  capable  of  communicating,  by  rubbing  each 
pair  or  couple  in  the  manner  I  formerly  described. 
Having  then  eight  bars  magnetic,  but  in  a  very 
small  degree,  I  take  two  pair,  which  I  join  together 
in  the  manner  represented  in  Fig.  133. 

By  uniting  the  two  bars  by  the  p-  oq 
poles  of  the  same  name,  I  form  but 
one  of  double  the  thickness,  and 
with  which  I  form  the  compass  A  C 
and  B  D ;  the  better  to  keep  up  the 
magnetic  current,  a  piece  of  soft 
iron  P  may  be  applied  at  the  top  C  D. 
The  legs  of  the  compass  may  be 
separated  as  far  as  is  judged  proper, 
and  I  rub  with  them,  one  after  the 
other,  the  remaining  bars,  which  will 
thereby  acquire  more  power  than  they  had  before, 
because  the  powers  of  the  first  are  now  united.  I 
have  now  only  to  join  these  two  pair  newly  rubbed 
in  the  same  manner,  and  by  rubbing  with  them,  one 
after  the  other,  the  two  pair  first  employed,  and  the 
power  of  these  will  be  considerably  increased.  I 
afterward  join  these  two  pair  together,  and  go  on 
rubbing  others,  in  order  to  augment  their  magnetic 
force,  and  still  two  pair  with  two  pair  alternately;  and 
by  repeating  this  operation,  the  magnetic  power  may 
be  carried  to  such  a  degree  as  to  become  insuscep- 
tible of  further  increase,  even  by  continuing  the  ope- 
ration. When  we  have  more  than  four  pair  of  such 
bars,  instead  of  two  pair,  three  may  be  joined  together 
for  the  purpose  of  rubbing  others ;  they  will  thereby 
be  sooner  carried  to  the  highest  degree  possible. 

The  greatest  obstacles  are  therefore  surmounted ; 
and  by  means  of  such  bars,  joined  together  by  two 
or  more  pairs,  we  may  rub  others  of  steel  properly 
hardened,  and  which  may  be  either  of  the  same  size, 
or  still  greater  than  the  first,  to  which  the  greatest 
power  of  which  they  are  susceptible  may  be  thus 
communicated. 

Beginning  with  small  bars  such  as  I  have  d& 


248 


MAGNETIC    FORCE. 


scribed,  these  operations  may  be  successively  applied 
to  bars  of  an  enormous  size,  and  made  of  the  hard- 
est steel,  which  is  less  liable  to  lose  the  magnetic 
power.  Only  it  is  to  be  observed,  that  for  the  pur- 
pose of  rubbing  large  bars,  several  pairs  ought  to  be 
joined  together,  whose  united  weight  should  be  at 
least  double  that  of  the  large  one.  But  it  would 
always  be  better  to  proceed  by  degrees,  and  to  rub 
each"  species  of  bars  with  bars  not  much,  smaller 
than  themselves,  or  it  may  be  sufficient  to  join  at 
most  two  pair :  for  when  we  are  obliged  to  join  more 
than  two  pair,  the  extremities  with  which  the  fric- 
tion is  performed  will  extend  too  far,  and  the  mag- 
netic matter  which  passes  that  way  will  itself  prevent 
its  being  directed  conformably  to  the  direction  of 
the  bar  that  is  rubbed ;  and  the  rather  that  it  enters 
the  bar  perpendicularly,  whereas  it  necessarily 
should  take  a  horizontal  direction. 

In  order  to  facilitate  this  change  of  direction,  it  is 
proper  that  the  magnetic  matter  should  be  led  to  it 
in  a  small  space,  and  in  a  direction  already  approach- 
ing to  that  which  it  ought  to  take  within  the  bar 
which  we  are  going  to  rub.  The  following  method, 
I  think,  might  be  effectual  for  this  purpose. 


Fig.  134  represents 
five  pair  of  bars  M  M, 
N  N,  joined  together, 
but  not  in  the  form  of  a 
compass.  There  is  at 
top  a  bar  of  soft  iron 
C  D,  to  keep  up  the  vor- 
tex; below,  I  do  not 
rub  immediately  with 
the  extremities  of  the 
bars,  but  I  case  these 
extremities  on  each 
side  in  a  foot  of  soft 
iron,  fastening  them  to 
it  with  screws  marked 
O.  Each  foot  is  bent 


Fig.  134. 


I 


!•   f™ 

V  J    y 


7 

/  *v 


ARTIFICIAL    MAGNETS.  249 

at  A  and  B,  so  that  the  direction  of  the  magnetic 
matter,  which  freely  pervades  these  feet,  already  has 
a  considerable  approximation  to  the  horizontal ;  so 
that  in  the  bar  to  be  rubbed  E  F  it  has  no  need 
greatly  to  change  its  direction.  I  have  no  doubt, 
that  by  means  of  these  feet  the  bar  E  F  will  receive 
a  much  greater  magnetic  power  than  if  we  rubbed 
immediately  by  the  extremities  of  the  bars,  the  depth 
of  whose  vertical  direction  naturally  opposes  the 
formation  of  horizontal  magnetic  canals  in  the  bar 
E  F.  It  is  likewise  possible,  in  practising  this 
method,  to  contract  or  extend  the  distance  of  the 
feet  A  and  B  at  pleasure. 

I  must  further  observe,  that  when  these  bars  lose 
in  time  their  magnetic  power,  it  is  easily  restored 
by  the  same  operation. 

1st  December,  1761. 


LETTER  LXXI. 

Construction  of  Artificial  Magnets  in  the  Form  of  a 
Horse-shoe. 

WHOEVER  wishes  to  make  experiments  on  the 
properties  of  the  loadstone  ought  to  be  provided 
with  a  great  number  of  magnetic  bars,  from  a  very 
small  up  to  a  very  large  size.  Each  may  be  con- 
sidered as  a  particular  magnet,  having  its  two  poles, 
the  one  north  and  the  other  south. 

You  must  have  considered  it  as  extremely  remark- 
able, that  by  the  interposition  of  the  magnetic  power, 
the  feeblest  which  can  be  supplied  by  a  wretched 
natural  loadstone,  or  by  a  pair  of  tongs  in  the  chim- 
ney corner,  which  have  acquired  by  length  of  time  a 
small  portion  of  magnetism,  we  should  be  enabled  to 
increase  that  power  to  such  a  degree  as  to  commu- 
nicate to  the  largest  bars  of  steel  the  highest  degree 
of  magnetic  force  of  which  they  are  susceptible.  It 


250 


ARTIFICIAL    MAGNETS. 


would  be  needless  to  add,  that  by  this  method  we 
are  enabled  to  construct  the  best  magnetic  needles, 
not  only  much  larger  than  the  common,  but  made 
of  a  steel  hardened  to  the  highest  degree,  which 
renders  them  more  durable.  I  have  only  a  few  words 
to  add  on  the  construction  of  artificial  magnets, 
which  have  usually  the  form  of  a  horse-shoe,  as  you 
must  no  doubt  have  seen. 

These  artificial  magnets  answer  the  same  purposes 
on  every  occasion  as  the  natural  ones,  with  this  ad- 
vantage in  their  favour,  that  we  can  have  them  much 
more  powerful,  by  giving  them  a  sufficient  magnitude. 
They  are  made  of  well  tempered  steel,  and  the  figure 
of  a  horse-shoe  seems  the  most  proper  for  keeping 
up  the  vortex.  When  the  mejchanic  has  finished 
his  work,  we  communicate  to  it  the  greatest  degree 
of  magnetic  power  of  which  it  is  susceptible,  by  means 
of  the  magnetic  bars,  of  which  I  have  given  a  de- 
scription. It  is  evident,  that  the  greater  this  magnet 
is,  the  larger  must  be  the  bars  we  employ :  and  this 
is  the  reason  why  we  should  be  provided  with  bars 
of  all  sizes. 

In  order  to  magnetize  a  horse-shoe  HIG,  Fig.  135, 
which  ought  to  be  of  steel  well  tern- 
pered,  we  place  on  the  table  a  pair 
of  magnetic  bars  A  C  and  B  D,  with 
their  supporters  of  soft  iron  applied 
on  both  sides,  but  of  which  the 
figure  represents  only  one  E  F,  the 
other  having  been  removed  to  make 
way  gradually  for  the  application  of 
the  feet  of  the  horse-shoe,  as  you 
see.  In  this  state,  the  magnetic 
matter  which  pervades  the  bars  will 
make  strong  efforts  to  pass  through 
the  horse-shoe,  the  poles  of  the  bars 
being  adapted  magnetically  to  those  _ 

of  the  horse-shoe ;  but  considering 
the  hardness  of  tempered  steel,  it  will  not  be  suffi- 


ARTIFICIAL   MAGNETS.  251 

cient  to  arrange  the  pores,  and  open  for  itself  a  pas- 
sage. The  same  means,  therefore,  must  be  em- 
ployed to  this  effect  which  were  prescribed  for  the 
magnetizing  of  bars.  We  take  a  compass  formed 
of  another  pair  of  magnetic  bars,  and  rub  them  in 
the  same  manner  over  the  horse-shoe;  magnetic 
canals  will  thereby  be  opened,  and  the  subtile  mat- 
ter of  the  bars,  by  pervading  it,  will  form  the  vortex 
of  that  fluid.  Particular  care  must  be  taken,  in  this 
operation,  that  the  legs  of  the  compass,  in  passing 
over  the  horse-shoe,  do  not  touch  the  extremities 
A  and  B  of  the  bars  ;  for  this  would  disturb  the  cur- 
rent of  the  magnetic  matter,  which  would  pass  im- 
mediately from  the  bars  into  the  legs  of  the  compass ; 
or  the  vortices  of  the  bars  and  of  the  compass  would 
mutually  derange  each  other. 

The  horse-shoe  will  thereby  acquire  very  great 
power,  being  pervaded  by  an  impetuous  magnetic 
current.  All  that  remains  to  be  done  is  to  detach 
the  bars  without  deranging  the  current.  If  they 
are  separated  violently,  the  magnetic  vortex  will  be 
destroyed,  and  the  artificial  magnet  will  retain  very 
little  power. 

The  canals  being  kept  up  no  longer  than  the  mag- 
netic matter  pervades  them,  it  must  be  concluded 
that  the  particles  which  form  these  canals  are  in  a 
forced  state,  and  that  this  state  subsists  only  while 
the  vortex  acts ;  and  that  as  soon  as  it  ceases,  these 
particles,  by  their  elasticity,  will  deviate  from  their 
forced  situation,  and  the  magnetic  canals  will  be 
interrupted  and  destroyed.  This  we  clearly  see  in 
the  case  of  soft  iron,  whose  pores  are  quickly  ar- 
ranged on  the  approach  of  a  magnetic  vortex,  but 
retain  scarcely  any  magnetic  power  when  removed 
out  of  the  vortex.  This  proves  that  the  pores  of 
iron  are  moveable,  but  endowed  with  an  elasticity 
which  changes  their  situation  as  soon  as  force  ceases. 
It  requires  length  of  time  to  fix  certain  pores  in  the 
position  impressed  on  them  by  the  magnetic  force, 


252  ARTIFICIAL    MAGNETS. 

which  takes  place  chiefly  in  bars  of  iron  long  exposed 
to  the  vortex  of  the  earth.  The  pores  of  steel  are 
much  less  flexible,  and  better  support  the  state  into 
which  they  have  been  forced :  they  are  however  liable 
to  some  derangement,  as  soon  as  force  ceases  to  act 
on  them ;  but  this  derangement  is  less  in  propor- 
tion to  the  hardness  of  the  steel.  For  this  reason 
artificial  magnets  ought  to  be  made  of  the  hardest 
steel :  were  they  to  be  made  of  iron,  they  would 
immediately  acquire,  on  being  applied  to  magnetic 
bars,  a  very  great  degree  of  power ;  but  the  moment 
you  detach  them,  all  that  power  would  disappear. 
Great  precaution  must  therefore  be  employed  in 
separating  from  the  bars  magnets  composed  of  well 
tempered  steel.  For  this  purpose,  before  the  sepa- 
ration, you  press  the  supporter,  which  is  of  very  soft 
iron,  in  the  direction  of  the  line  M  N,  Fig.  136,  tak- 
ing particular  care  not  to  touch  the  pig.  135. 
bars  with  it,  for  this  would  mar  the 
whole  process,  and  oblige  you  to  re- 
peat the  operation.  On  the  applica- 
tion of  the  supporter,  a  considerable 
portion  of  the  magnetic  matter  which 
is  circulating  in  the  magnet  G  H I  will 
make  its  way  through  the  supporter, 
and  form  a  separate  vortex,  which  will  continue  after 
the  magnet  is  detached  from  the  bars. 

Afterward,  you  press  the  supporter  slowly  forward 
over  the  legs  of  the  magnet  to  the  extremities,  as 
represented  in  the  figure,  and  in  this  state  permit  it 
to  rest  for  some  time,  that  the  vortex  may  be  allowed 
to  settle.  The  supporter  is  likewise  furnished  with 
a  weight  P,  which  may  be  increased  every  day ;  it 
being  always  understood  that  the  supporter  is  to  be 
so  perfectly  adjusted  to  the  feet  of  the  magnet  as  to 
touch  them  in  all  points.* 

5th  December,  1761. 

*  The  laws  of  magnetism  have  been  ably  investigated  during  the  last 
ten  years,  and  many  highly  interesting  facts  have  been  added  to  our  pro- 


ON   DIOPTRICS.  253 


LETTER  LXXIT. 

On  Dioptrics  ;  Instruments  which  that  Science  supplies .' 
of  Telescopes  and  Microscopes.  Different  Figures 
given  to  Glasses  or  Lenses. 

THE  wonders  of  dioptrics  will  now,  I  think,  fur- 
nish a  subject  worthy  of  your  attention.  This  science 
provides  us  with  two  kinds  of  instruments  composed 
of  glass,  which  serve  to  extend  our  sphere  of  vision, 
by  discovering  objects  which  would  escape  the  naked 
eye. 

There  are  two  cases  in  which  the  eye  needs  assist- 

vions  knowledge  of  this  department  of  physics.  It  has  been  conclu- 
sively shown  that  the  magnetic  fluid  is,  if  not  identical  with  the  electric, 
so  intimately  associated  with  it  as  to  appear  to  be  the  same  thing  modified 
only  by  some  peculiarities  of  motion  or  mode  of  excitement.  The  im- 
portant discovery  was  made  by  Professor  CErsted,  of  Copenhagen,  that 
when  a  current  of  Voltaic  electricity  is  passing  along  the  surface  of  a  bar 
of  copper,  tin,  lead,  iron,  or  other  metal,  the  bar  possesses  magnetic  prop- 
erties, and  will  cause  an  immediate  deviation  of  a  magnetic  needle  sus- 
pended near  it ;  that  it  has  its  north  and  south  poles,  the  situation  of 
which  depends  on  the  direction  of  the  electric  current ;  that  these  poles 
are  immediately  changed  by  changing  the  direction  of  the  current ;  that 
the  bar  of  metal,  which,  thus  conducting  the  electric  fluid,  will  attract  iron 
filings,  and  in  short  convert  iron  or  steel  into  magnets,  in  the  same  man- 
ner as  a  natural  loadstone  or  artificial  magnet.  So  effectual  is  this  mode 
of  producing  artificial  magnets  that  Professor  Henry,  of  Albany,  relates 
an  experiment  performed  by  himself  and  Dr.  Ten  Eyck,  in  which  a  bar  of 
iron  bent  in  the  form  of  a  horse-shoe,  and  weighing  59  j  Ibs.  avoirdupois, 
being  surrounded  with  a  coil  of  copper  wire  728  feet  long,  and  the  ends  of 
the  wire  connected  with  galvanic  batteries  containing  4  7-9ths  square  feet 
of  surface,  the  iron  became  instantly  so  powerfully  magnetized  by  the 
revolution  of  the  electric  current  around  it  as  to  sustain  a  weight  at- 
tached to  its  armature  or  lifter  of  2000  Ibs. — (Vide  American  Journal  of 
Science,  vol.  xx.  p.  201.) 

The  discovery  of  CErsted  and  the  numerous  and  successful  investiga- 
tions of  the  nature  of  the  connexion  between  electricity  and  magnetism 
have  laid  the  foundation  of  a  new  branch-of  physics,  called  electro-mag- 
netism. A  spark,  similar  to  the  electric  spark,  has  been  obtained  from  an 
iron  magnet  alone,  unconnected  with  an  electric  or  galvanic  battery. — 
(American  Journal  of  Science,  vol.  xxii.  p.  410.) 

Of  the  identity  of  the  two  agents  there  can  therefore  be  no  longer  a 
doubt.  The  theory  of  our  author  of  course  is  untenable.— Am.  Ed. 

VOL.  II.— Y 


254  ON   DIOPTRICS. 

ance :  the  first  is,  when  objects  are  too  distant  to 
admit  of  our  seeing  them  distinctly ;  such  are  the 
heavenly  bodies,  respecting  which  the  most  important, 
discoveries  have  been  ,made  by  means  of  dioptrical 
instruments.  You  will  please  to  recollect  what  I 
have  said  concerning  the  satellites  of  Jupiter,  which 
assist  us  in  the  discovery  of  the  longitude  ;  they  are 
visible  only  with  the  aid  of  good  telescopes ;  and 
those  of  Saturn  require  telescopes  of  a  still  better 
construction. 

There  are,  besides,  on  the  surface  of  the  earth 
objects  very  distant,  which  it  is  impossible  for  us  to 
see,  and  to  examine  in  detail,  without  the  assistance 
of  telescopes,  which  represent  them  to  us  in  the 
same  manner  as  if  they  were  near.  These  dioptri- 
cal glasses  or  instruments  for  viewing  distant  bodies 
are  denominated  telescopes.  • 

The  other  case  in  which  the  eye  needs  assistance 
is  when  the  object,  though  sufficiently  near,  is  too 
small  to  admit  of  a  distinct  examination  of  its  parts. 
If  we  wished,  for  example,  to  discover  all  the  parts 
of  the  leg  of  a  fly,  or  of  any  insect  still  smaller, — if 
we  were  disposed  to  examine  the  minuter  particles 
of  the  human  body,  such  as  the  smallest  fibres  of  the 
muscles,  or  of  the  nerves,  it  would  be  impossible  to 
sueceed  without  the  help  of  certain  instruments 
called  microscopes,  which  represent  small  objects  in 
the  same  manner  as  if  they  were  a  hundred  or  a 
thousand  times  greater. 

Here,  then,  are  two  kinds  of  instruments,  tele- 
scopes and  microscopes,  furnished  by  dioptrics  for 
assisting  the  weakness  of  our  sight.  A.  few  ages 
only  have  elapsed  since  these  instruments  were  in- 
vented ;  and  from  the  era  of  that  invention  must  be 
dated  the  most  important  discoveries  in  astronomy 
by  means  of  the  telescope,  and  in  physics  by  the 
microscope. 

These  wonderful  effects  are  produced  merely  by 
the  figure  given  to  bits  of  glass,  and  the  happy  com- 


ON    DIOPTRICS.  255 

bination  of  two  or  more  glasses,  which  we  denomi- 
nate lenses.  Dioptrics  is  the  science  that  unfolds 
the  principles  on  which  such  instruments  are  con- 
structed, and  the  uses  to  which  they  are  applied ; 
and  you  will  please  to  recollect  that  it  turns  chiefly 
on  the  direction  which  rays  of  light  take  on  passing 
through  transparent  media  of  a  different  quality ;  on 
passing,  for  example,  from  air  into  glass  or  water, 
and  reciprocally,  from  glass  or  water  into  air. 

As  long  as  the  rays  are  propagated  through  the 
same  medium,  as  for  example  air,  they  preserve  the 
same  direction,  in  the  straight 
lines  L  A,  L  B,  L  C,  L  D,  Fig.  128, 
drawn  from  the  luminous  point  L, 
whence  these  rays  issue ;  and 
when  they  anywhere  meet  an 
eye  they  enter  into  it,  and  there 
paint  an  image  of  the  object  from 
which  they  proceeded.  In  this 
case  the  vision  is  denominated 
simple,  or  natural ;  and  represents  to  us  the  objects 
as  they  really  are.  The  science  which  explains  to 
us  the  principles  of  this  vision  is  termed  optics. 

But  when  the  rays,  before  they  enter  into  the  eye, 
are  reflected  on  a  finely  polished  surface,  such  as  a 
mirror,  the  vision  is  no  longer  natural ;  as  in  this 
case  we  see  the  objects  differently,  and  in  a  different 
place,  from  what  they  really  are.  The  science  which 
explains  the  phenomena  presented  to  us  by  this 
vision  from  reflected  rays  is  termed  catoptrics.  It, 
too,  supplies  us  with  instruments  calculated  to  extend 
the  sphere  of  our  vision ;  and  you  are  acquainted 
with  such  sorts  of  instruments,  which,  by  means  of 
one  or  two  mirrors,  render  us  the  same  services  as 
those  constructed  with  lenses.  These  are  what  we 
properly  denominate  telescopes ;  but  in  order  to  dis- 
tinguish them  from  the  common  perspectives,  which 
are  composed  only  of  glasses,  it  would  he  better  to 


256  ON   DIOPTRICS. 

call  them  catoptric  or  reflecting  telescopes.  This 
mode  of  expression  would  at  least  be  more  accurate ; 
for  the  word  telescope  was  in  use  before  the  dis- 
covery of  reflecting  instruments,  and  then  meant 
the  same  thing  with  perspective. 

I  propose  at  present  to  confine  myself  entirely  to 
dioptrical  instruments,  of  which  we  have  two  sorts, 
telescopes  and  microscopes.  In  the  construction 
of  both  we  employ  glasses  formed  after  different 
manners,  the  various  sorts  of  which  I  am  going  to 
explain.  They  are  principally  three,  according  to 
the  figure  given  to  the  surface  of  the  glass. 

The  first  is  the  plane,  when  the  surface  of  a  glass 
is  plane  on  both  sides,  as  that  of  a  common  mirror 
If  you  were  to  take,  for  example,  a  piece  of  looking- 
glass,  and  to  separate  from  it  the  quicksilver  which 
adheres  to  its  farther  surface,  you  would  have  a  glass 
both  of  whose  surfaces  are  plane,  and  of  the  same 
thickness  throughout. 

The  second  is  the  convex ;  a  glass  of  this  denomi- 
nation is  more  raised  in  the  middle  than  towards  the 
edge. 

The  third  is  the  concave ;  such  a  glass  is  hollow 
towards  the  middle,  and  rises  towards  the  edge. 

Of  these  three  different  figures  which  maybe  given 
to  the  surface  of  a  glass,  are  produced  the  six  species 
of  glasses  represented  in  Fig.  133. 

Fig.  133. 


I.  The  plane  glass  has  both  its  surfaces  plane. 

II.  The  plano-convex  glass  has  one  surface  plane 
and  the  other  convex. 


DIFFERENT    KINDS    OF    LENSES.  257 

III.  The  plano-concave  has  one  surface  plane  and 
the  other  concave. 

IV.  The  convexo-convex,  or  double  convex,  has  both 
surfaces  convex. 

V.  The  convexo-concave,  or  meniscus,  has  one  sur- 
face convex  and  the  other  concave. 

VI.  Finally,  the  concavo-concave,  or  double  concave, 
has  both  surfaces  concave. 

It  is  proper  to  remark,  that  the  figure  represents 
the  section  of  these  glasses  or  lenses. 
8th  December,  1761. 


LETTER  LXXIII. 

Difference  of  Lenses  with  respect  to  the  Curve  of  their 
Surfaces.     Distribution  of  Lenses  into  three  Classes. 

FROM  what  I  have  said  respecting  the  convex  and 
concave  surfaces  of  lenses,  you  will  easily  compre- 
hend that  their  form  may  be  varied  without  end, 
according  as  the  convexity  and  concavity  are  greater 
or  less.  There  is  only  one  species  of  plane  surfaces, 
because  a  surface  can  be  plane  in  one  manner  only; 
but  a  convex  surface  may  be  considered  as  making 
part  of  a  sphere,  and  according  as  the  radius  or 
diameter  of  that  sphere  is  greater  or  less,  the  con- 
vexity will  differ ;  and  as  we  represent  lenses  on 
paper  by  segments  of  a  circle,  according  as  these 
circles  are  greater  or  less,  the  form  of  lenses  must 
be  infinite,  with  respect  both  to  the  convexity  an<J 
concavity  of  their  surfaces. 

As  to  the  manner  of  forming  and  polishing  glasses, 
all  possible  care  is  taken  to  render  their  figure  ex- 
actly circular  or  spherical ;  for  this  purpose  we  em- 
ploy basins  of  metal  formed  by  the  turning  machine, 
on  a  spherical  surface,  both  inwardly  and  outwardly. 
Y2 


258  DIFFERENT    KINDS    OF    LENSES. 

Let  A  E  B  D  F  C,  Fig.  137,  be  the 
form  of  such  a  basin,  which  shall  have  Fig.  137- 
two  surfaces,  A  E  B  and  C  F  D,  each 
of  which  may  have  its  separate  ra- 
dius ;  when  a  piece  of  glass  is  rubbed 
on  the  concave  side  of  the  basin  A  E  B,  it  will  become 
convex ;  but  if  it  is  rubbed  on  the  convex  side  C  F  D, 
it  will  become  concave.  Sand,  or  coarse  emery,  is 
at  first  used  in  rubbing  the  glass  on  the  basin,  till  it 
has  acquired  the  proper  form ;  and  after  that  a  fine 
species  of  emery,  or  pumice-stone,  to  give  it  the  last 
polish. 

In  order  to  know  the  real  figure  of  the  surfaces 
of  a  lens,  you  have  only  to  measure  the  radius  of  the 
surface  of  the  basin  on  which  that  lens  was  formed ; 
for  the  true  measure  of  the  convexity  and  concavity 
of  surfaces,  is  the  radius  of  the  circle  or  sphere 
which  corresponds  to  them,  and  t>f  which  they  make 
a  part. 

Thus,  when  it  is  said  that  the  radius  of  the  con- 
vex surface  A  E  B,  Fig.  138,  is  three  inches,  the 

Fig.  138. 


meaning  is,  that  A  E  B  is  an  arch  of  a  circle  described 
with  a  radius  of  three  inches,  the  other  surface  A  B 
being  plane. 

That  I  may  convey  a  still  clearer  idea  of  the  dif- 
ference of  convexities,  when  their  radii  are  greater 
or  less,  I  shall  here  present  you  with  several  figures 
of  different  convexity,  Fig.  139. 

Fig.  139. 

Two  Inches. 

One  Inch 


Half  an  Icch.  Third  of  an  Inch.  Fifth  of  an  Inch 

f ^  <£^  £Z± 

Sixth  of  an  Inch.  Eighth  of  an  Inch. 


DIFFERENT    KINDS    OF   LENSES.  259 

From  this  you  see,  that  the  smaller  the  radius  is 
the  greater  is  the  curve  of  the  surface,  or  the  greater 
its  difference  from  the  plane ;  on  the  contrary,  the 
greater  the  radius  is,  the  more  the  surface  approaches 
to  a  plane,  or  the  arch  of  the  circle  to  a  straight 
line.  If  the  radius  were  made  still  greater,  the  curve 
would  at  length  become  hardly  perceptible.  You 
scarcely  perceive  it  in  the  arch  M  N,  Fig.  138,  the 
radius  of  which  is  six  inches,  or  half  a  foot ;  and  if 
the  radius  were  still  extended  to  ten  or  a  hundred 
times  the  magnitude,  the  curve  would  become  alto- 
gether imperceptible  to  the  eye. 

But  this  is  by  no  means  the  case  as  to  dioptrics  , 
and  I  shall  afterward  demonstrate,  that  though  the 
radius  were  a  hundred  or  a  thousand  feet,  and  the 
curve  of  the  lens  absolutely  imperceptible,  the  effect 
would  nevertheless  be  abundantly  apparent.  The 
radius  must  indeed  be  inconceivably  great  to  pro- 
duce a  surface  perfectly  plane :  from  which  you  may 
conclude,  that  a  plane  surface  might  be  considered 
as  a  convex  surface  whose  radius  is  infinitely  great, 
or  as  a  concave  of  a  radius  infinitely  great.  Here  it 
is  that  convexity  and  concavity  are  confounded,  so 
that  the  plane  surface  is  the  medium  which  separates 
convexity  from  concavity.  But  the  smaller  the 
radii  are,  the  greater  and  more  perceptible  do  the 
convexities  and  concavities  become ;  and  hence  we 
say,  reciprocally,  that  a  convexity  or  concavity  is 
greater  in  proportion  as  its  radius,  which  is  the 
measure  of  it,  is  smaller. 

However  great  in  other  respects  maybe  the  variety 
we  meet  with  in  lenses  or  glasses,  according  as  their 
surfaces  are  plane,  convex,  or  concave,  and  this  in 
an  infinity  of  different  manners ;  nevertheless,  with 
respect  to  the  effect  resulting  from  them  in  dioptrics, 
they  may  be  reduced  to  the  three  following  classes : — 

The  first  comprehends  glasses  which  are  every- 
where of  an  equal  thickness ;  whether  their  two  sur- 


260  DIFFERENT    KINDS    OF    LENSES. 

faces  be  plane  and  parallel  to  each  other,  Fig.  140, 
or  the  one  convex  and  the  other  concave,  but  con- 

Fig-.  140. 


centric,  or  described  round  the  same  centre,  Fig. 
141,  so  that  the  thickness  shall  remain  everywhere 
the  same.  It  is  to  be  remarked  respecting  glasses 

Fig.  141. 


of  this  class,  that  they  produce  no  change  in  the 
appearance  of  the  objects  which  we  view  through 
them;  the  objects  appear  exactly  the  same  as. if 
nothing  interposed ;  accordingly,  they  are  of  no 
manner  of  use  in  dioptrics.  This  is  not  because  the 
rays  which  enter  into  these  glasses  undergo  no  re- 
fraction, but  because  the  refraction  at  the  entrance 
is  perfectly  straightened  on  going  off,  so  that  the 
rays,  after  having  passed  through  the  glass,  resume 
the  same  direction  which  they  had  pursued  before 
they  reached  it.  Glasses,  therefore,  of  the  other 
two  classes,  on  account  of  the  effect  which  they 
produce,  constitute  the  principal  object  of  dioptrics. 
The  second  class  of  lenses  contains  those  which 
are  thicker  at  the  middle  than  at  the  edge,  Fig.  142. 

Fig.  142. 


Their  effect  is  the  same,  as  long  as  the  excess  of 
the  thickness  of  the  middle  over  that  of  the  edge  has 
the  same  relation  to  the  magnitude  of  the  lens.  All 
lenses  of  this  class  are  commonly  denominated  con- 


EFFECT  OF  CONVEX  LENSES.        26  . 

vex,  as  convexity  predominates,  though  otherwise 
one  of  their  surfaces  may  be  plane,  and  even  con- 
cave. 

The  third  class  contains  all  those  lenses  which 
are  thicker  at  the  edge  than  in  the  middle,  Fig.  143, 

Fig.  143. 


which  all  produce  a  similar  effect,  depending  on  the 
excess  of  thickness  towards  the  edge  over  that  in  the 
middle.  As  concavity  prevails  in  all  such  lenses, 
they  are  simply  denominated  -concave.  They  must 
be  carefully  distinguished  from  those  of  the  second 
class,  which  are  the  convex. 

Lenses  of  these  two  last  classes  are  to  be  the  sub- 
ject of  my  following  Letters,  in  which  I  shall  en- 
deavour to  explain  their  effects  in  dioptrics. 

12th  December,  1761. 


LETTER  LXXIV. 

Effect  of  Convex  Lenses. 

IN  order  to  explain  the  effect  produced  by  both 
convex  and  concave  lenses  in  the  appearance  of  ob- 
jects, two  cases  must  be  distinguished ;  the  one  when 
the  object  is  very  far  distant  from  the  lens,  and  the 
other  when  it  is  nearer. 

But  before  I  enter  on  the  explanation  of  this,  I 
must  say  a  few  words  on  what  is  called  the  axis  of 
the  lens.  As  the  two  surfaces  are  represented  by 
segments  of  a  circle,  you  have  only  to  draw  a  straight 
line  through  the  centres  of  the  two  circles ;  this  line 
is  named  the  axis  of  the  lens.  In  Fig.  144,  the  cen- 


262  EFFECT    OF    CONVEX   LENSES. 

tre  of  the  arch  A  E  B  being  at  C,  and 

that  of  the  arch  A  F  B  at  D,the  straight 

line  C  D  is  denominated  the  axis  of 

the  lens  A  B ;  and  it  is  easy  to  see 

that  this  axis   passes   through   the 

middle  of  it.     The  same  thing  would 

apply  if  the  surfaces  of  the  lens  were  ,£  F 

concave.     But  if  one  is  plane,  the       vr 

axis  will  be  perpendicular  to  it,  pass-  jf 

ing  through  the  centre  of  the  other 

surface. 

Hence  it  is  obvious  that  the  axis  passes  through 
the  two  surfaces  perpendicularly,  and  that  accord- 
ingly a  ray  of  light  coming  in  the  direction  of  the 
axis  will  suffer  no  refraction,  because  rays  passing 
from  one  medium  into  another  are  not  broken  or 
refracted,  except  when  they  do  not  enter  in  a  per- 
pendicular direction. 

It  may  likewise  be  proved  that  all  other  rays  pass- 
ing through  the  middle  of  the  lens  O  undergo  no 
refraction,  or  rather  that  they  again  become  parallel 
to  themselves. 

It  must  be  considered,  in  order  to  comprehend  the 
reason  of  this,  that  at  the  points  E  and  F  the  two 
surfaces  of  the  lens  are  parallel  to  each  other,  for 
the  angle  M  E  B  which  the  ray  M  E  makes  with  the 
arch  of  the  circle  E  B,  or  its  tangent  at  E,  is  per- 
fectly equal  to  the  angle  P  F  A,  which  this  same 
ray  produced,  or  F  P  makes  with  the  arch  of  the 
circle  A  F,  or  its  tangent  at  F :  you  recollect  that  two 
such  angles  are  denominated  alternate,  and  that  it  is 
demonstrated,  when  the  alternate  angles  are  equal, 
that  the  straight  lines  are  parallel  to  each  other; 
consequently,  the  two  tangents  at  E  and  at  F  will  be 
parallel,  and  it  will  be  the  same  thing  as  if  the  ray 
M  E  F  P  passed  through  a  lens  whose  two  surfaces 
were  parallel  to  each  other.  Now  we  have  already 
seen  that  rays  do  not  change  their  direction  in  pass- 
ing- through  such  a  lens. 


EFFECT  OF  CONVEX  LENSES.       263 

Having  made  these  remarks,  let  us  now  consider 
a  convex  lens  A  B,  Fig.  145,  whose  axis  is  p-  U5 
the  straight  line  O  E  F  P ;  and  let  us  sup-  *  ^ 
pose  that  there  is  in  this  line,  at  a  great 
distance  from  the  lens,  an  object  or  lu- 
minous point  O,  which  diffuses  rays  in 
all  directions :  some  of  these  will  pass 
through  our  lens  A  B,  such  as  O  M,  0  E, 
and  O  N ;  of  which  that  in  the  middle,  O  E, 
will  undergo  no  refraction,  but  will  con- 
tinue its  direction  through  the  lens  in  the 
same  produced  straight  line  F  I  P.  The 
other  two  rays,  O  M  and  O  N,  in  passing 
through  the  lens  towards  the  edge,  will 
be  refracted  both  at  entering  and  depart- 
ing, so  that  they  will  somewhere"  meet 
the  axis,  as  at  I,  and  afterward  continue 
their  progress  in  the  direction  I  Q  and  I R. 
It  might  likewise  be  demonstrated  that 
all  the  rays  which  fall  between  M  and  N 
will  be  refracted,  so  as  to  meet  with  the 
axis  in  the  same  point  I.  Therefore,  the 
rays  which,  had  no  lens  interposed,  would 
have  pursued  their  rectilineal  direction 

0  M  and  O  N,  will,  after  the  refraction, 

pursue  other  directions,  as  if  they  had  taken  their 
departure  from  the  point  I:  and  if  there  were  an 
eye  somewhere  at  P,  it  would  be  affected  just  as  if 
the  luminous  point  were  actually  at  I,  though  there 
be  no  reality  in  this.  You  have  only  to  suppose  for 
a  moment,  that  there  is  at  I  a  real  object,  which 
diffusing  its  rays,  would  be  equally  seen  by  an  eye 
placed  at  P,  as  it  now  sees  the  object  at  O  by  means 
of  the  rays  refracted  by  the  lens,  because  there  is  at 

1  an  image  of  the  object  0,  and  the  lens  A  B  there 
represents  the  object  O,  or  transports  it  nearly  to  I. 
The  point  0  is  therefore  no  longer  the  object  of 
vision,  but  rather  its  image,  represented  at  I ;  for 
this  is  now  its  immediate  obiect. 


264  DISTANCE    OF   THE 

This  lens,  then,  produces  a  very  considerable 
change :  an  object  very  remote  O  is  suddenly  trans- 
ported to  I,  from  which  the  eye  must  undoubtedly 
receive  a  very  different  impression  from  what  it 
would  do  if,  withdrawing  the  lens,  it  were  to  view 
the  object  O  immediately.  Let  O  be  considered  as 
a  star,  the  point  O  being  supposed  extremely  distant, 
the  lens  will  represent  at  I  the  image  of  that  star, 
but  an  image  which  it  is  impossible  to  touch,  and 
which  has  no  reality,  as  nothing  exists  at  I,  unless 
it  be  that  the  rays  proceeding  from  the  point  O  are 
collected  there  by  the  refraction  of  the  lens.  Nei- 
ther is  it  to  be  imagined  that  the  star  would  appear 
to  us  in  the  same  manner  as  if  it  really  existed  at  I. 
How  could  a  body  many  thousands  of  times  bigger 
than  the  earth  exist  at  a  point  I?  Our  senses  would 
be  very  differently  struck  by  it.  We  must  carefully 
remark,  then,  that  an  image  only  is  represented  at  I, 
like  that  of  a  star  represented  in  the  bottom  of  the 
eye,  or  that  which  we  see  in  a  mirror,  the  effect  of 
which  has  nothing  to  surprise  us. 

15th  December,  1761. 


LETTER  LXXV. 

The  same  Subject:  Distance  of  the  Focus  of  Convex 
Lenses.    ' 

I  MEAN  to  employ  this  Letter  in  explaining  the  effect 
produced  by  convex  lenses,  that  is,  such  as  are 
thicker  at  the  middle  than  at  the  edge.  The  whole 
consists  in  determining  the  change  which  rays  un- 
dergo in  their  progress,  on  passing  through  such  a 
glass.  In  order  to  place  this  subject  in  its  clearest 
light,  two  cases  must  be  carefully  distinguished ;  the 
one  when  the  object  is  very  distant  from  the  lens, 
and  the  other  when  it  is  at  no  great  distance.  I 


FOCUS  OF  CONVEX  LENSES. 


265 


begin  with  considering  the  first  case,  that  is,  when 
the  object  is  extremely  remote  from  the  lens. 

In  Fig.  146,  M  N  is  the  convex  lens,  ^v.  145 
and  the  straight  line  O  A  B I  S  its  axis, 
passing  perpendicularly  through  the 
middle.  I  remark,  by-the-way,  that 
this  property  of  the  axis  of  every 
lens,  that  of  passing  perpendicularly 
through  its  middle,  conveys  the  justest 
idea  of  it  that  we  are  capable  of  form- 
ing. Let  us  now  conceive  that  on 
this  axis  there  is  somewhere  at  O  an 
object  O  P,  which  I  here  represent  as 
a  straight  line,  whatever  figure  it  may 
really  have;  and  as  every  point  of 
this  object  emits  its  rays  in  all  direc- 
tions, we  confine  our  attention  to 
those  which  fall  on  the  lens. 

My  remarks  shall  be  at  present  fur- 
ther limited  to  the  rays  issuing  from 
the  point  O,  situated  in  the  very  axis 
of  the  lens.  The  figure  represents 
three  of  these  rays,  O  A,  O  M,  and  O  N, 
the  first  cf  which,  O  A  passing  through 
the  middle  of  the  lens,  undergoes  no 
change  of  direction,  but  proceeds,  after  having  passed 
through  the  lens,  in  the  same  straight  line  BIS,  that 
is,  in  the  axis  of  the  lens ;  but  the  other  two  rays, 
O  M  and  0  N,  undergo  a  refraction  both  on  entering 
into  the  glass  and  leaving  it,  by  which  they  are 
turned  aside  from  their  first  direction,  so  as  to  meet 
somewhere  at  I  with  the  axis,  from  which  they  will 
proceed  in  their  new  direction,  in  the  straight  lines 
M I Q  and  N I R ;  so  that  afterward,  when  they  shall 
meet  an  eye,  they  will  produce  in  it  the  same  effect 
as  if  the  point  0  existed  at  I,  as  they  preserve  the 
same  direction.  For  this  reason,  the  convex  lens  is 
said  to  transport  the  object  O  to  I ;  but  in  order  to 
distinguish  this  point  I  from  the  real  point  O,  the 

VOL.  II.— Z 


266  DISTANCE    OF    THE 

former  is  called  the  image  of  the  latter,  which  in  it* 
turn  is  denominated  the  object. 

This  point  I  is  very  remarkable,  and  when  the  ob- 
ject O  is  extremely  distant,  the  image  of  it  is  like- 
wise denominated  the  focus  of  the  lens,  of  which  1 
shall  explain  the  reason.  If  the  sun  be  the  object  at 
O,  the  rays  which  fall  on  the  lens  are  all  collected  at 
I ;  and  being  endowed  with  the  quality  of  heating,  it 
is  natural  that  the  concourse  of  so  many  rays  at.  I 
should  produce  a  degree  of  heat  capable  of  setting 
on  fire  any  combustible  matter  that  may  be  placed 
there.  Now,  the  place  where  so  much  heat  is  col- 
lected we  call  the  focus ;  the  reason  of  this  denomi- 
nation with  respect  to  convex  lenses  is  evident. 
Hence,  too,  a  convex  lens  is  denominated  a  burning- 
glass,  the  effects  of  which  you  are  undoubtedly  well 
acquainted  with.  I  only  remark,  that  this  property 
of  collecting  the  rays  of  the  sun  in  a  certain  point, 
called  their  focus,  is  common  to  all  convex  lenses  : 
they  likewise  collect  the  rays  of  the  moon,  of  the 
stars,  and  of  all  very  distant  bodies ;  though  their 
force  is  too  small  to  produce  any  heat,  we  neverthe- 
less employ  the  same  term,  focus :  the  focus  of  a 
glass,  accordingly,  is  nothing  else  but  the  spot  where 
the  image  of  very  distant  objects  is  represented ;  to 
which  this  condition  must  still  be  added,  that  the 
object  ought  to  be  situated  in  the  very  axis  of  the 
lens  ;  for  if  it  be  out  of  the  axis,  its  image  will  like- 
wise be  represented  out  of  the  axis.  I  shall  have 
occasion  to  speak  of  this  afterward. 

It  may  be  proper  still  further  to  subjoin  the  fol- 
lowing remarks  respecting  the  focus : — 

1.  As  the  point  0,  or  the  object,  is  infinitely  dis- 
tant, the  rays  O  M,  O  A.  and  O  N  may  be  considered 
as  parallel  to  each  other ;  and,  for  the  same  reason, 
parallel  to  the  axis  of  the  lens. 

2.  The   focus  I,  therefore,  is  the  point  behind 
the  glass  where  the  rays  parallel  to  the  axis  which 


FOCUS  OF  CONVEX  LENSES.        267 

fell  on  the  lens  are  collected  by  the  refraction  of  the 
lens. 

3.  The  focus  of  a  lens,  and  the  spot  where  the 
image  of  an  object,  infinitely  distant,  and  situated 
in  the  axis  of  the  lens,  is  represented,  are  the  same 
thing. 

4.  The  distance  of  the  point  I  behind  the  lens,  that 
is,  the  length  of  the  line  B  I,  is  called  the  distance  of 
the  focus  of  the  lens.     Some  authors  call  it  the  focal 
distance,  or  focal  length. 

5.  Every  convex  lens  has  its  particular  distance 
of  focus-— one  greater,  another  less — which  is  easily 
ascertained  by  exposing  the  lens  to  the  sun,  and  ob- 
serving where  the  rays  meet. 

6.  Lenses  formed  by  arches  of  small  circles,  have 
their  focuses  very  near  behind  them;   but  those 
whose  surfaces  are  arches  of  great  circles  have  more 
distant  focuses. 

7.  It  is  of  importance  to  know  the  focal  distance 
of  every  convex  lens  employed  in  dioptrics  ;  and  it 
is  sufficient  to  know  the  focus  in  order  to  form  a 
judgment  of  all  the  effects  to  be  expected  from  it, 
whether  in  the  construction  of  telescopes  or  micro- 
scopes. 

8.  If  we  employ  lenses  equally  convex  on  both 
sides,  so  that  each  surface  shall  correspond  to  the 
same  circle,  then  the  radius  of  that  circle  gives 
nearly  the  focal  distance  of  that  lens ;  thus,  to  make 
a  burning-glass  which  shall  burn  at  the  distance  of 
a  foot,  you  have  only  to  form  the  two  surfaces 
arches  of  a  circle  whose  radius  is  one  foot. 

9.  But  when  the  lens  is  plano-convex,  its  focal 
distance  is  nearly  equal  to  the  diameter  of  the  circle 
which  corresponds  to  the  convex  surface. 

Acquaintance  with  these  terms  will  facilitate  the 
knowledge  of  what  I  have  further  to  advance  on  this 
subject. 

19th  December,  1761. 


268  DISTANCE   OF   THE 

LETTER  LXXVI. 

Distance  of  the  Image  of  Objects. 

HAVING  remarked  that  an  object  infinitely  distant 
is  represented  by  a  convex  lens  in  the  very  focus, 
provided  the  object  be  in  the  axis  of  the  lens,  I  pro- 
ceed to  nearer  objects,  but  always  situated  in  the 
axis  of  the  glass ;  and  I  observe,  first,  that  the  nearer 
the  object  approaches  to  the  lens  the  farther  the 
image  retires. 

Let  us  accordingly  suppose  that  F,  Fig.  147. 
Fig.  147,  is  the  focus  of  the  lens  MM, 
so  that  when  an  object  is  infinitely  dis- 
tant before  the  glass,  or  at  the  top  of 
the  figure,  the  image  shall  be  repre- 
sented at  F ;  on  bringing  the  pbje*ct 
nearer  to  the  glass,  and  placing  it  suc- 
cessively at  P,  Q,  R,  the  image  will  be 
represented  at  the  points  p,  q,  r,  more  * fS 

distant  from  the  lens  than  the  focus : 
in  other  words,  if  A  P  is  the  distance 
of  the  object,  B  p  will  be  the  distance 
of  the  image ;  and  if  A  Q  is  the  dis- 
tance  of  the  object,  B  q  will  be  that  of 
the  image ;  and  the  distance  B  r  of  the 
image  will  correspond  to  the  distance 
A  R  of  the  object. 

There  is  a  rule  by  which  it  is  easy 
to  calculate  the  distance  of  the  image 
behind  the  lens  for  every  distance  of 
the  object  before  it,  but  I  will  not  tire 
you  with  a  dry  exposition  of  this  rule ; 
it  will  be  sufficient  to  remark,  in  gene- 
ral, that  the  more  the  distance  of  the  object  be- 
fore the  glass  is  diminished,  the  more  is  the  distance 
of  the  image  behind  it  increased.  I  shall  to  this 


IMAGE    OF    OBJECTS. 


269 


subjoin  the  instance  of  a  convex  lens  whose  focal 
distance  is  six  inches,  or  of  a  lens  so  formed  that 
if  the  distance  of  the  object  is  infinitely  great,  the 
distance  of  the  image  behind  the  lens  shall  be  pre- 
cisely six  inches ;  now,  on  bringing  the  object  nearer 
to  the  lens,  the  image  will  retire,  according  to  the 
gradations  marked  in  the  following  table : 


Distance 

of  the  Object. 

Distance 

of  the  Image. 

Infinity. 

6 

42 

7 

h 

24 

8 

18 

9 

15 

10 

12 

12 

10 

15 

9 

18 

8 

24 

7 

42 

6 

Infinity. 

Thus,  the  object  being  42  inches  distant  from  the 
lens,  the  image  will  fall  at  the  distance  of  7  inches, 
that  is,  one  inch  beyond  the  focus.  If  the  object  is 
at  the  distance  of  24  inches,  the  image  will  be  re- 
moved to  the  distance  of  8  inches  from  the  lens, 
that  is,  two  inches  beyond  the  focus  ;  and  so  of  the 
rest. 

Though  these  numbers  are  applicable  only  to  a 
lens  whose  focal  distance  is  6  inches,  some  general 
consequences  may,  however,  be  deduced  from  them. 

1.  If  the  distance  of  the  object  is  infinitely  great 
the  image  falls  exactly  in  the  focus.  * 

2.  If  the  distance  of  the  object  is  double  the  dis- 
tance of  the  focus,  the  distance  of  the  image  will 
likewise  be  double  the  distance  of  the  focus  ;  in  other 
words,  the  object  and  the  image  will  be  equally  dis- 
tant from  the  lens.     In  the  example  above  exhibited; 

.<•  2 


270 


IMAGE    OF    OBJECTS. 


the  distance  of  the  object  being  12  inches,  that  of 
the  image  is  likewise  12  inches. 

3.  When  the  object  is  brought  so  near  the  lens 
that  the  distance  is  precisely  equal  to  that  of  the 
focus,  say  6  inches,  as  in  the  preceding  example, 
then  the  image  retires  to  an  infinite  distance  behind 
the  lens. 

4.  It  is  likewise  observable  in  general,  that  the 
distance  of  the  object  and  that  of  the  image  recip- 
rocally correspond  ;  or  if  you  put  the  object  in  the 
place  of  the  image,  it  will  fall  in  the  place  of  the 
object. 

5.  If,  therefore,  the  lens  M  M,  Fig.  148, 
collects  at  I  the  rays  which  issue  from 
the  point  O,  the  same  lens  will  likewise 
collect    at   O   rays    issuing   from  the 
point  I. 

6.  It  is  the  consequence  of  a  great 
principle  in  dioptrics,  in  virtue  of  which 
it  may  be  maintained  that  whatever  are 
the  refractions  which  rays  have  under- 
gone in  passing  through  several  refract- 
ing media,  they  may  always  return  in  the 
same  direction. 

This  truth  is  of  much  importance  in  the  know- 
ledge of  lenses  :  thus,  when  I  know,  for  example, 
that  a  lens  has  represented,  at  the  distance  of  8 
inches,  the  image  of  an  object  24  inches  distant,  I 
may  confidently  infer,  that  if  the  object  were  8  inches 
distant,  the  same  lens  would  represent  its  image  at 
the  distance  of  24  inches. 

It  is  further  essential  to  remark,  that  when  the 
distance  of  the  object  is  equal  to  that  of  the  focus, 
the  image  will  suddenly  retire  to  an  infinite  distance ; 
which  perfectly  harmonizes  with  the  relation  existing 
between  the  object  and  the  image. 

You  will  no  doubt  be  curious  to  know  in  what 
place  the  image  will  be  represented  when  the  object 
is  brought  still  nearer  to  the  lens,  so  that  its  distance 


MAGNITUDE    OF   IMAGES.  271 

shall  become  less  than  that  of  the  focus.  This  ques- 
tion is  the  more  embarrassing,  that  the  answer  must 
be,  the  distance  of  the  image  will  in  this  case  be 
greater  than  infinity,  since  the  nearer  the  object  ap- 
proaches the  lens  the  farther  does  the  image  retire. 
But  the  image  being  already  infinitely  distant,  how 
is  it  possible  that  distance  should  be  increased  1  The 
question  might  undoubtedly  puzzle  philosophers,  but 
is  of  easy  solution  to  the  mathematician.  The  image 
will  pass  from  an  infinite  distance  to  the  other  side 
of  the  lens,  and  consequently  will  be  on  the  same 
side  with  the  object.  However  strange  this  answer 
may  appear,  it  is  confirmed,  not  only  by  reasoning, 
but  by  experience,  so  that  it  is  impossible  to  doubt 
of  its  solidity ;  to  increase  beyond  infinity  is  the  same 
thing  with  passing  to  the  other  side :  this  is  unques- 
tionably a  real  paradox. 
22d  December,  1761. 


LETTER  LXXVII. 

Magnitude  of  Images. 

You  can  no  longer  doubt  that  every  convex  lens 
must  represent  somewhere  the  image  of  an  object 
presented  to  it ;  and  that  in  every  case  the  place 
of  the  image  varies  as  much  according  to  the  dis- 
tance of  the  object  as  according  to  the  focal  distance 
of  the  lens :  but  a  very  important  article  remains 
yet  to  be  explained — I  mean  the  magnitude  of  the 
image. 

When  such  a  lens  represents  to  us  the  image  of 
the  sun,  of  the  moon,  or  of  a  star,  at  the  distance  of 
a  foot,  you  are  abundantly  sensible  that  these  images 
must  be  incomparably  smaller  than  the  objects  them- 
selves. A  star  being  much  greater  than  the  whole 
earth,  how  is  it  possible  that  an  image  of  such  mag- 


272 


MAGNITUDE    OF    IMAGES. 


Fig.  149. 


nitude  should  be  represented  to  us  at  the  distance  of 
a  foot  1  But  the  star  appearing  to  us  only  as  a  point, 
the  image  represented  by  the  lens  likewise  resembles 
a  point,  and  consequently  is  infinitely  smaller  than 
the  object  itself. 

There  are,  then,  in  every  representation  made  by 
lenses,  two  things  to  be  considered ;  the  one  respects 
the  place  where  the  image  is  represented,  and  the 
other  the  real  magnitude  of  the  image,  which  may 
be  very  different  from  that  of  the  object.  The  first 
being  sufficiently  elucidated,  I  proceed  to  furnish 
you  with  a  very  simple  rule,  by  which  you  will  be 
enabled  in  every  case  to  determine  what  must  be 
the  magnitude  of  the  image  represented  by  the 
lens. 

Let  O  P,  Fig.  149,  be  any  object 
whatever  situated  on  the  axis  of  the 
convex  lens  M  N ;  we  must  first  look 
for  the  place  of  the  image,  which  is 
at  I,  so  that  the  point  I  shall  be  the 
representation  of  the  extremity  O  of 
the  object,  as  the  rays  issuing  from 
the  point  O  are  there  collected  by 
the  refraction  of  the  lens.  Let  us 
now  see  in  what  place  will  be  repre- 
sented the  other  extremity  P  of  the 
object ;  for  this  purpose  let  us  con- 
sider the  rays  P  M,  P  A,  P  N,  which, 
issuing  from  the  point  P,  fall  on  the 
lens.  I  observe  that  the  ray  P  A, 
which  passes  through  the  middle  of 
the  lens,  does  not  change  its  direc- 
tion, but  continues  its  progress  in  the 
straight  line  A  K  S ;  it  will  be  there- 
fore somewhere  in  this  line,  at  K, 
that  the  other  rays  P  M  and  P  N 
will  meet :  in  other  words,  the  point 
K  will  be  the  image  of  the  other  extremity  P  of  the- 
object,  the  point  I  being  that  of  the  extremity  0 : 


MAGNITUDE    OF    IMAGES. 


273 


i50. 


hence  it  is  easy  to  conclude  that  I  K  will  be  the 
image  of  the  object  0  P  represented  by  the  lens. 

In  order,  then,  to  determine  the  magnitude  of  this 
image,  having  found,  the  place  I,  you  have  only  to 
draw  from  the  extremity  P  of  the  object,  through  A, 
the  middle  of  the  lens,  the  straight  line  P  A  K  S,  and 
to  raise  from  I  the  line  I  K  perpendicular  to  the  axis, 
and  this  line  I  K  will  be  the  image  in  question  ;  it  is 
evident  from  this  that  the  image  is  reversed,  so  that 
if  the  line  O  R  were  horizontal,  and  the  object  O  P 
a  man,  the  image  would  have  the  head  K  undermost, 
and  the  feet  I  uppermost. 

On  this  I  subjoin  the  following  remarks  : 

1.  The  nearer  the  image  is  to  the  lens,  the  smaller 
it  is  ;  and  the  more  remote  it  is,  the  greater  its  mag- 
nitude.    Thus,  O  P,  Fig.  150,  being 

the  object  placed  on  the  axis  before 
the  lens  M  N,  if  the  image  fell  at  Q, 
it  would  be  smaller  than  if  it  fell  at 
R,  S,  or  T.  For,  as  the  straight  line 
P  A  £,  drawn  from  the  summit  of  the 
object  P,  through  the  middle  of  the 
lens,  always  terminates  the  image, 
at  whatever  distance  it  may  be,  it  is 
evident  that  among  the  lines  Q  y,  R  r, 
S  s,  T  t,  the  first  Q  q  is  the  smallest, 
and  that  the  others  increase  in  pro- 
portion as  they  remove  from  the 
lens. 

2.  There  is  one  case  in  which  the 
image  is  precisely  equal  to  the  object  : 
it  is  when  the  distance  of  the  image  is 
equal  to  that  of  the  object  ;  and  this 
takes  place,  as  I  have  already  re- 
marked, when  the  distance  of  the 
object  A  O  is  double  that  of  the  focus 

of  the  lens  ;  the  image  will  then-  be  T  r,  so  that  the 
distance  B  t  is  equal  to  A  O.  \  ou  have  only  then 
to  consider  the  two  triangles  GAP  and  T  A  <, 


274  MAGNITUDE    OF    IMAGES. 

which  having  the  opposite  angles  at  the  point  A,  as 
well  as  the  sides  A  O  and  A  T,  equal  each  to  each, 
as  likewise  the  angles  at  O  and  T,  which  are  both 
right  angles ;  these  two  triangles  will  be  every  way 
equal,  and  consequently  the  side  T  t,  which  is  the 
image,  will  be  equal  to  the  side  O  P,  which  is  the 
object. 

3.  If  the  image  were  twice  farther  from  the  lens 
than  the  object,  it  would  be  double  the  object ;  and 
in  general,  as  many  times  as  the  image  is  farther 
from  the  lens  than  the  object,  so  many  times  will 
it  be    greater  than  the   object.     For  the  nearer 
you  bring  the  object  to  the  glass,  the  farther  the 
image  retires,  and  consequently  the  greater  it  be- 
comes. 

4.  The  contrary  takes  place  when  the  image  is 
nearer  the  lens  than  the  object ;  it  is  then  as  many 
times  smaller  than  the  object   as  it  is  nearer  the 
lens  than  the  object  is.     If,  then,  the 'distance  of 
the  image  were  one  thousand  times  less  than  that 
of  the  object,  it  would  likewise  be  one  thousand 
times  smaller. 

5.  Let  us  apply  this  to  burning-glasses,  which, 
being  exposed  to  the  sun,  represent  its  image  in  the 
focus,  or  rather  represent  the  focus,  that  is,  the  lumi- 
nous and  brilliant  circle,  which  burns,  and  which  is 
nothing  else  but  the  image  of  the  sun  represented  by 
the  lens.     You  will  no  longer  be  surprised,  then,  at 
the  smallness  of  the  image,  notwithstanding  the  pro- 
digious magnitude  of  the  sun,  it  being  as  many  times 
smaller  in  the  focus  than  the  real  sun,  as  the  dis- 
tance of  the  sun  from  the  lens  is  greater  than  that 
of  the  image. 

6.  Hence  likewise  it  is  evident,  that  the  greater  is 
the  distance  of  the  focus  of  a  burning-glass,  the 
more  brilliant  also  is  the  circle  in  the  focus,  that 
is,  the  greater  will  be  the  image  of  the  sun ;  and  the 
diameter  of  the  focus  is  always  about  one  hundred 
times  smaller  than  the  distance  of  the  focus  from 
the  lens. 


BURNING-GLASSES.  275 

I  shall  afterward  explain  the  different  uses  which 
may  be  made  of  convex  lenses ;  they  are  all  suffi- 
ciently curious  to  merit  attention. 

26th  December,  1761. 


LETTER  LXXVIII. 

Burning-glasses. 

THE  first  use  of  convex  lenses  is  their  employ- 
ment as  burning-glasses,  the  effect  of  which  must 
appear  altogether  astonishing,  even  to  those  who 
already  have  some  acquaintance  with  natural  philo- 
sophy. In  fact,  who  could  believe  that  the  image 
of  the  sun  simply  should  be  capable  of  exciting  such 
a  prodigious  degree  of  heat  1  But  your  surprise  will 
cease,  if  you  please  to  pay  some  attention  to  the 
following  reflections : — 

1.  Let  M  N,  Fig.  151,  be  a  burn- 
ing-glass,  which  receives  on  its 
surface  the  rays  of  the  sun  R,  R,  R, 
refracted  in  such  a  manner  as  to. 
present  at  F  a  small  luminous  cir- 
cle, which  is  the  image  of  the  sun, 
and  so  much  smaller  as  it  is  nearer 
to  the  glass. 

2.  All  the  rays  of  the  sun,  which 

fall  on  the  surface  of  the  glass  are  collected  in  the 
small  space  of  the  focus  F;  their  effect,  accord- 
ingly, must  in  that  space  be  as  many  times  greater 
as  the  surface  of  the  glass  exceeds  the  magnitude 
of  the  focus,  or  of  the  sun's  image.  We  say  that 
the  rays,  which  were  dispersed  over  the  whole 
surface  of  the  glass,  are  concentrated  in  the  small 
space  F. 

3.  The  rays  of  the  sun  having  a  certain  degree  of 
heat,  they  exert  their  power  in  a  very  sensible  man- 
ner at  the  focus ;  it  is  possible  even  to  calculate  how 


276  BURNING-GLASSES. 

many  times  the  heat  at  the  focus  must  exceed  the 
natural  heat  of  the  sun's  rays :  we  have  only  to 
observe  how  many  times  the  surface  of  the  glass  is 
greater  than  the  focus. 

4.  If  the  glass  were  not  greater  than  the  focus, 
the  heat  would  not  be  stronger  at  the  focus  than  any- 
where else ;  hence  we  must  conclude,  that  in  order 
to  the  production  of  a  strong  heat  by  a  burning- 
glass,  it  is  not  sufficient  that  it  should  be  convex,  or 
that  it  should  represent  the  image  of  the  sun ;  it 
must  besides  have  a  surface  which  several  times 
exceeds  the  magnitude  of  the  focus,  which  is  smaller 
in  proportion  as  it  is  nearer  to  the  glass. 

5.  France  is  in  possession  of  the  most  excellent 
burning-glass :  it  is  three  feet  in  diameter,  and  its 
surface  is  calculated  to  be  nearly  two  thousand  times 
greater  than  the  focus,  or  the  image  of  the  sun  which 
it  represents.*    It  must  produce,  therefore,  in  the 
focus,  a  heat  two  thousand  times  greater  than  that 
which  we  feel  from  the  sun.     Its  effects  are  accord- 
ingly prodigious  :  wood  of  every  kind  is  in  a  moment 
set  on  fire;  metals  are  melted  in  a  few  minutes; 
and,  in  general,  the  most  ardent  fire  which  we  are 
capable  of  producing  is  not  once  to  be  compared 
with  the  vehement  heat  of  this  focus. 

6.  The  heat  of  boiling  water  is  calculated  to  be 
about  thrice  greater  than  what  we  feel  from  the  rays 
of  the  sun  in  summer ;  or,  which  amounts  to  the 
same  thing,  the  heat  of  boiling  water  is  thrice  greater 
than  the  natural  heat  of  the  blood  in  the  human 
body.     But  in  order  to  melt  lead,  we  must  have  a 
heat  thrice  greater  than  is  requisite  to  make  water 

*  The  lens  here  alluded  to  was,  we  believe,  one  of  Tschirnhausen's, 
that  the  Duke  of  Orleans  purchased  for  the  \cademy  of  Sciences.  A 
more  powerful  burning  lens,  however,  was  afterward  made  in  England 
by  Mr.  Parker,  which  cost  above  700Z.  It  had  2  feet  8£  inches  of  clear 
diameter.  Its  thickness  at  the  centre  was  3^  inches,  and  its  focal  length 
6  feet  8  inches  in  diameter.  It  was  made  of  flint-glass.  This  celebrated 
lens  is  now  at  Pekin.— See  Edinburgh  Encyclopaedia,  article  Burning 
Instruments,  vol.  v.  p.  141.— Ed. 


BURNING-GLASSES.  277 

boil ;  and  to  melt  copper,  a  heat  still  thrice  greater 
is  necessary.  To  melt  gold  requires  a  much  higher 
degree  of  heat.  Heat,  then,  one  hundred  times 
greater  than  that  of  our  blood  is  capable  of  melting 
gold ;  how  far  then  must  a  heat  two  thousand  times 
greater  exceed  the  force  of  our  ordinary  fires  1 

7.  But  how  are  these  prodigious  effects  produced 
by  the  rays  of  the  sun  collected  in  the  focus  of  a 
burning-glass?     This  is  a  very  difficult  question, 
with  respect  to  which  philosophers  are  very  much 
divided.     Those  who  maintain  that  the  rays  are  an 
emanation  from  the  sun,  darted  with  the  amazing 
velocity  which  I  formerly  described,  are  not  greatly 
embarrassed  for  a  solution ;  they  have  only  to  say 
that  the  matter  of  the  rays,  striking  bodies  with 
violence,  must  totally  break  and  destroy  their  minute 
particles.     But  this  opinion  is  no  longer  admitted  in 
sound  philosophy. 

8.  The  other  system,  which  makes  the  nature  of 
light  to  consist  in  the  agitation  of  the  ether,  appears 
little  adapted  to  explain  these  surprising  effects  of 
burning-glasses.     On  carefully  examining,  however, 
all  the  circumstances,  we  shall  soon  be  convinced  of 
the  possibility  of  this.     The  natural  rays  of  the  sun, 
as  they  fall  on  bodies,  excite  the  minute  particles  of 
the  surface  to  a  concussion,  or  motion  of  vibration, 
which,  in  its  turn,  is  capable  of  exciting  new  rays ; 
and  by  these  the  body  in  question  is  rendered  visible. 
And  a  body  is  illuminated  only  so  far  as  these 
proper  particles  are  put  into  a  motion  of  vibration 
so  rapid  as  to  be  capable  of  producing  new  rays  in 
the  ether. 

9.  It  is  clear,  then,  that  if  the  natural  rays  of  the 
sun  have  sufficient  force  to  agitate  the  minute  par- 
ticles of  bodies,  those  which  are  collected  in  the 
focus  must  put  the  particles  which  they  meet  there 
into  an  agitation  so  violent  that  their  mutual  adhe- 
sion is  entirely  dissolved,  and  the  body  itself  com- 
pletely destroyed,  which  is  the  effect  of  fire.     For  if 

VOL.  II.— A  a 


278  THE    CAMERA    OBSCURA. 

the  body  is  combustible,  as  wood,  the  dissolution  of 
these  minute  particles,  joined  to  the  most  rapid  agi- 
tation, makes  a  considerable  part  of  it  to  fly  off  into 
air  in  the  form  of  smoke,  and  the  grosser  particles 
remain  in  the  form  of  ashes.  Fusible  bodies,  as 
metals,  become  liquid  by  the  dissolution  of  their  par- 
ticles, whence  we  may  comprehend  how  fire  acts  on 
bodies ;  it  is  only  the  adhesion  of  their  minutest  par- 
ticles which  is  attacked,  and  the  particles  themselves 
are  thereby  afterward  put  into  the  most  violent  agita- 
tion. Here,  then,  is  a  very  striking  effect  of  burn- 
ing-glasses, which  derives  its  origin  from  the  nature 
of  convex  lenses.*  There  are  besides  many  wonder- 
ful effects  to  be  described. 
28th  December,  1761. 


LETTER  LXXIX. 

The  Camera  Obscura. 

WE  likewise  employ  convex  lenses  in  the  camera 
obscura,  and  by  means  of  them  all  external  objects 
are  presented  in  the  darkened  room  on  a  white  sur- 
face, in  their  natural  colours,  in  such  a  manner  that 
landscapes  and  public  buildings,  or  objects  in  general, 
are  represented  in  much  greater  perfection  than 
the  power  of  the  pencil  is  capable  of  producing. 
Painters  accordingly  avail  themselves  of  this  method, 
in  order  to  draw  with  exactness  landscapes  and  other 
objects  which  are  viewed  at  a  distance.  The  camera 
obscura,  then,  which  is  the  subject  of  this  Letter, 
is  represented  at  E  F  G  H,  Fig.  152,  closely  shut  up 

*  In  the  work  already  quoted,  in  p,  262,  note,  I  have  shown  how  burn- 
ing lenses  may  be  constructed  of  any  size,  by  building  them,  as  it  were, 
of  separate  zones,  each  zone  consisting  of  different  segments,  which  are 
ground  and  polished  separately.  By  this  means  the  central  parts  of 
the  burning  lens  are  much  less  thick  than  when  the  lens  is  of  one  piece, 
and  the  error  of  the  spherical  aberration  may  be  in  a  great  measure  cor- 
rected.—See  the  Edinburgh  Philosophical  Journal,  vol.  viii.  p.  160.— Ed. 


THE    CAMERA    OBSCURA.  279 

Fig.  152. 


on  all  sides,  except  one  little  round  aperture  made 
in  one  of  the  window-shutters,  in  which  is  fixed  a 
convex  lens,  of  such  a  focus  as  to  throw  the  image 
of  external  objects,  say  the  tree  O  P,  exactly  on  the 
opposite  wall  F  G,  at  o  p.  A  white  and  moveable 
table  is  likewise  employed,  which  is  put  in  the  place 
of  the  images  represented. 

The  rays  of  light,  therefore,  can  be  admitted  into 
the  chamber  only  through  the  aperture  M  N,  in 
which  the  lens  is  fixed,  without  which  total  darkness 
would  prevail. 

Let  us  now  consider  the  point  P  of  any  object, 
say  the  stem  of  our  tree  O  P.  Its  rays  P  M,  P  A, 
P  N,  will  fall  on  the  lens  M  N,  and  be  refracted  by 
it,  so  as  to  meet  again  at  the  point  p  on  the  wall,  or 
on  a  white  table*  placed  there  for  the  purpose. 
This  point  p  will  consequently  receive  no  other  rays 
but  such  as  proceed  from  the  point  P ;  and  in  like 
manner  every  other  point  of  the  table  will  receive 
only  the  rays  which  proceed  from  the  corresponding 
point  of  the  object ;  and  reciprocally,  to  every  point 

*  The  table  should  be  made  of  stucco,  or  plaster  of  Paris,  ground  very 
tmnoothly,  and  ought  to  be  concave,  that  every  part  of  it  may  be  equally 
distant  from  the  lens. — Ed. 


280  THE    CAMERA   OBSCURA. 

of  the  external  object  will  correspond  a  point  on  the 
table,  which  receives  those  rays,  and  no  other.  If 
the  lens  were  to  be  removed  from  the  aperture  M  N, 
the  table  would  be  illuminated  in  quite  a  different 
manner;  for  in  that  case  every  point  of  the  object 
would  diffuse  its  rays  over  the  whole  table,  so  that 
every  point  of  the  table  would  be  illuminated  at 
once  by  all  the  external  objects,  whereas  at  present 
it  is  so  by  one  only,  that  whose  rays  it  receives : 
from  this  you  will  easily  comprehend  that  the  effect 
must  be  quite  different  from  what  it  would  be  if  the 
rays  entered  simply  by  the  aperture  M  N  into  the 
chamber. 

Let  us  now  examine  somewhat  more  closely 
wherein  this  difference  consists  ;  and  let  us  first  sup- 
pose that  the  point  P  of  the  object  is  green ;  the 
point  of  the  table  p  will  therefore  receive  only  those 
green  rays  of  the  object  P,  and  these,  reuniting  on 
the  wall  or  table,  will  make  a  certain 'impression, 
which  here  merits  consideration.  For  this  purpose 
you  will  please  to  recollect  the  following  propo- 
sitions, which  I  had  formerly  the  honour  of  explain- 
ing to  you : — 

1.  Colours  differ  from  each  other  in  the  same 
manner  as  musical  sounds ;  each  colour  is  produced 
by  a  determinate  number  of  vibrations,  which  in  a 
given  time  are  excited  in  the  ether.     The  green 
colour  of  our  point  P  is  accordingly  appropriated  to 
a  certain  number  of  vibrations,  and  would  no  longer 
be  green  were  these  vibrations  more  or  less  rapid. 
Though  we  do  not  know  the  number  of  vibrations 
which  produce  such  or  such  a  colour,  we  may  how- 
ever be  permitted  to  suppose  here  that  green  requires 
twelve  thousand  vibrations  in  a  second  ;  and  what  we 
affirm  of  this  number,  twelve  thousand,  may  likewise 
be  easily  understood  of  the  jeal  number,  whatever 
it  be. 

2.  This  being  laid  down,  the  point  p  on  the  white 
table  will  be  struck  by  a  motion  of  vibration,  of  which 


THE    CAMERA    OBSCURA.  281 

twelve  thousand  will  be  completed  in  a  second. 
Now,  I  have  remarked  that  the  particles  of  a  white 
surface  are  all  of  such  a  nature  as  to  receive  every 
sort  of  agitation,  more  or  less  rapid ;  whereas  those 
of  a  coloured  surface  are  adapted  to  receive  only  that 
degree  of  rapidity  which  corresponds  to  their  colour. 
And  as  our  table  is  white,  the  point  p  in  it  will  be 
excited  to  a  motion  of  vibration  corresponding  to  the 
colour  of  green ;  in  other  words,  it  will  be  agitated 
twelve  thousand  times  in  a  second. 

3.  As  long  as  the  point  j»,  or  the  particle  of  the 
white  surface  which  exists  there,  is  agitated  with  a 
similar  motion,  this  will  be  communicated  to  the  par- 
ticles of  the  ether  which  surround  it;  and  this  motion, 
diffusing  itself  in  all  directions,  will  generate  rays  of 
the  same  nature,  that  is  to  say  green;  just  as  in 
music,  the  sound  of  a  certain  note,  say  C,  agitates  a 
string  wound  up  to  the  same  tone,  and  makes  ifr  emit 
a  sound  without  being  touched. 

4.  The  point  p  of  the  white  table  will  accordingly 
produce  green  rays,  as  if  it  were  died  or  painted  that 
colour ;  and  what  I  affirm  of  the  pointy  will  equally 
take  place  with  respect  to  all  the  points  of  the  illu- 
minated table,  which  will  produce  all  the  rays,  each 
of  the  same  colour  with  that  of  the  object  whose 
image  it  represents.     Every  point  of  the  table  will 
therefore  become  visible,  under  a  certain  colour,  as 
if  it  were  actually  painted  that  colour. 

5.  You  will  perceive,  then,  on  the  table,  all  the 
colours  of  the  external  objects,  the  rays  of  which 
will  be  admitted  into  the  chamber  through  the  lens ; 
each  point  in  particular  will  appear  of  the  colour  of 
that  point  of  the  object  which  corresponds  to  it,  and 
you  will  see  on  the  table  a  combination  of  various 
colours,  disposed  in  the  same  order  as  you  see  them 
in  the  objects  themselves ;  that  is  to  say,  a  repre- 
sentation, or  rather  the  perfect  picture,  of  all  the  ob- 
jects on  the  outside  of  the  dark  chamber  which  are 
before  the  lens  N  N. 

Aa2 


282  THE    CAMERA    OBSCURA. 

6.  All  these  objects  will,  however,  appear  reversed 
on  the  table,  as  you  will  conclude  from  what  I  have 
said  in  my  foregoing  Letters.     The  under  part  of  the 
tree  0  will  be  represented  at  o,  and  the  summit  P  at 
p;  for,  in  general,  each  object  must  be  represented 
on  the  white  table  in  the  place  which  is  the  termi- 
nation of  the  straight  line  drawn  from  the  object  P 
through  the  middle  of  the  lens  A  :  that  which  is  up- 
ward will  consequently  be  represented  downward, 
and  that  which  is  to  the  left  will  be  to  the  right ;  in 
a  word,  every  thing  will  be  reversed  in  the  picture ; 
the  representation  will  nevertheless  be  more  exact 
and  more  perfect  than  the  most  accurate  painter  is 
capable  of  producing.  • 

7.  You  will  further  remark,  that  this  picture  will 
be  so  much  smaller  than  the  objects  themselves  in 
proportion  as  the  focus  of  the  lens  is  shorter.    Lenses 
of  a  short  focus  will  accordingly  give  the  objects  in 
miniature;   and  if  you  would  wish  to  have  them 
magnified,  you  must  employ  lenses  of  a  longer  focus, 
or  which  represent  the  images  at  a  greater  distance. 

8.  In  order  to  contemplate  these  representations 
more  at  ease,  the  rays  may  be  intercepted  by  a  mir- 
ror, from  which  they  are  reflected,  so  as  to  represent 
the  whole  picture  on  a  horizontal  table ;  and  this  is 
of  peculiar  advantage  when  we  wish  to  copy  the 
images.* 

2d  January,  1762. 

*  The  lens  is  sometimes  ground  on  the  anterior  surface  of  a  thick  piece 
of  glass,  the  posterior  surface  of  which  is  ground  flat,  and  inclined  45°  to 
the  axis  of  the  lens.  The  picture  is  therefore  reflected  on  a  horizontal 
table,  without  the  use  of  a  mirror,  and  the  image  is  much  more  perfect) 
as  the  light  is  totally  reflected.— Ed. 


THE    CAMERA    OBSCURA.  283 

LETTER  LXXX. 

Reflections  on  the  Representation  in  the  Camera  Olscura. 

THOUGH  you  can  no  longer  entertain  any  doubt 
respecting  the  representations  made  in  a  dark  cham- 
ber by  means  of  a  convex  lens,  I  hope  the  following 
reflections  will  not  appear  superfluous,  as  they  serve 
to  place  this  subject  in  a  clearer  light : — 

1.  The  chamber  must  be  completely  darkened,  for 
were  the  light  admitted  the  white  table  would  be 
visible,  and  the  particles  of  its  surface,  already  agi- 
tated, would  be  incapable  of  receiving  the  impression 
of  the  rays  which  unite  to  form  the  images  of  exter- 
nal objects.     Though,  however,  the  chamber  were  a 
little  illuminated,  still  something  of  the  representation* 
would  appear  on  the  table,  but  by  no  means  so  vivid 
as  if  the  chamber  were  entirely  dark. 

2.  We  must  carefully  distinguish  the  picture  repre- 
sented on  the  white  table  from  the  image  which  the 
lens  in  virtue  of  its  own  nature  represents,  as  I  have 
formerly  explained.     It  is  very  true,  that  placing  the 
table  in  the  very  place  where  the  image  of  the  ob- 
jects is  formed  by  the  lens,  this  image  will  be  con- 
founded by  the  picture  we  perceive  on  the  table; 
these  two  things  are  nevertheless  of  a  nature  entirely 
different:  the  image  is  only  a  spectre  or  shadow 
floating  in  the  air,  which  is  visible  but  in  certain 
places ;  whereas  the  representation  is  a  real  picture, 
which  every  one  in  the  chamber  may  see,  and  to 
which  duration  alone  is  wanting. 

3.  In  order  the  more  clearly  to  elucidate  this  differ- 
ence, you  have  only  to  consider  carefully  the  nature 
of  the  image  0,  Fig.  153,  represented  by  the  convex 
lens  M  N,  the  object  being  at  O.     This  image  is 
nothing  else  but  the  place  in  which  the  rays  O  M, 
O  C,  0  N,  of  the  object,  after  having  passed  through 


284  THE    CAMERA    OBSCURA. 

Fig.  153. 


the  lens,  meet  by  refraction,  and  thence  continue 
their  direction  as  if  they  proceeded  from  the  point 
o,  though  they  really  originated  from  O,  and  by  no 
means  from  o. 

4.  Hence  the  image  is  visible  only  to  eyes  situated 
somewhere  within  the  angle  R  o  Q,  as  at  S,  where 
an  eye  will  actually  receive  the  rays  which  come  to 
it  from  the  point  o.     But  an  eye  situated  out  of 
this  angle,  as  at  F  or  V,  will  see  nothing  at  all  of  it, 
because  no  one  of  the  rays  collected  at  o  is  directed 
towards  it :  the  image  at  0,  therefore,  differs  very 
essentially  from  a  real  object,  and  is  visible  only  in 
certain  places. 

5.  But  if  a  white  table  is  placed  at  o,  and  its  sur- 
face at  this  point  o  is  really  excited  to  an  agitation 
similar  to  that  which  takes  place  in  the  object  0, 
this  spot  o  of  the  surface  itself  generates  rays  which 
render  it  visible  everywhere.     Here,  then,  is  the 
difference  between  the  image  of  an  object  and  its 
representation  made  in  a  camera  obscura :  the  image 
is  visible  only  in    certain   places,   namely,  those 
through  which  are  transmitted  the  rays  that  origin- 
ally proceed  from  the  object ;  whereas  the  picture, 
or  representation  formed  on  the  white  table,  is  seen 
by  its  own  rays,  excited  by  the  agitation  of  the  par- 
ticles of  its  surface,  and  consequently  visible  in 
every  place  of  the  camera  obscura. 


THE    CAMERA    OBSCURA.  285 

6.  It  is  likewise  evident  that  the  white  table  must 
absolutely  be  placed  exactly  in  the  place  of  the  image 
formed  by  the  lens,  in  order  that  every  point  of  the 
table  may  receive  no  other  rays  except  such  as  pro- 
ceed from  a  single  point  of  the  object;  for  if  other 
rays  were  likewise  to  fall  upon  it,  they  would  dis- 
turb the  effect  of  the  former,  or  render  the  repre- 
sentation confused. 

7.  Were  the  lens  to  be  entirely  removed,  and  free 
admission  given  to  the  rays  into  the  dark  chamber, 
the  white  table  would  be  illuminated  by  it,  but  no 
picture  would  be  visible.     The  rays  of  the  different 
objects  would  fall  on  every  point  of  the  table,  with- 
out expressing  any  one  determinate  image.     The 
picture,  accordingly,  which  we  see  in  a  camera  ob- 
scura,  on  a  white  surface,  is  the  effect  of  the  convex 
lens  fixed  in  the  shutter :  this  it  is  which  collects 
anew,  in  a  single  point,  all  the  rays  that  proceed 
from  one  point  of  the  object. 

3.  A  very  singular  phenomenon  is  here  however 
observable,  when  the  aperture  made  in  the  window- 
shutter  of  the  dark  chamber  is  very  small ;  for  though 
no  lens  be  applied  you  may  nevertheless  perceive, 
on  the  opposite  partition,  the  images  of  external  ob- 
jects, and  even  with  their  natural  colours ;  but  the 
representation  is  very  faint  and  confused,  and  if  the 
aperture  is  enlarged,  this  representation  entirely 
disappears.  I  shall  explain  this  phenomenon. 

In  Fig.  154,  M  N  is 
the  small  aperture  through 
which  the  rays  of  external 
objects  are  admitted  into  the 
dark  chamber  E  F  G  H. 
The  wall  F  G  opposite  to 
the  aperture  is  white,  the 
better  to  receive  the  impres- 
sion of  rays  of  all  sorts. 

Let  the  point  O  be  an  object,  of  which  the  rays 
O  M,  0  N  alone,  with  those  which  fall  between 


286  OF    THE    MAGIC   LANTERN, 

them,  can  enter  into  the  chamber.  These  rays  will 
be  confined  to  the  small  space  o  o  of  the  wall,  and 
will  illuminate  it.  This  space  o  o  will  be  so  much 
smaller,  or  approach  the  nearer  to  a  point,  in  pro- 
portion as  the  aperture  M  N  is  small :  if  then  this 
aperture  were  very  small,  we  should  have  the  effect 
already  described,  according  to  which  every  point 
of  th,e  white  table  receives  only  the  rays  proceeding 
from  a  single  point  of  the  object:  there  would  be 
produced,  of  consequence,  a  representation  similar 
to  that  which  is  produced  by  the  application  of  a 
convex  lens  to  an  aperture  in  the  window-shutter. 
But  in  the  present  case,  the  aperture  being  of  a  cer- 
tain extent,  every  point  O  of  the  object  will  illumi- 
nate a  certain  small  space  o  o  on  the  wall,  and  agitate 
it  by  its  rays.  The  same  thing,  then,  nearly,  would 
take  place,  as  if  a  painter,  instead  of  making  points 
with  a  fine  pencil,  should  with  a  coarsS  one  make 
spots  of  a  certain  magnitude,  attending,  however, 
to  design  and  colouring :  the  representation  made  on 
the  wall  will  have  a  resemblance  to  this  sort  of 
daubing ;  but  it  will  be  clearer  in  proportion  to  the 
smallness  of  the  aperture  by  which  the  rays  are  ad- 
mitted. 

5th  January,  1762. 


LETTER  LXXXI. 

Of  the  Magic  Lantern,  and  Solar  Microscope. 

THE  camera  obscura  has  properly  no  effect  except 
on  very  distant  objects,  but  you  will  easily  compre- 
hend that  its  application  may  be  equally  extended 
to  nearer  objects.  For  this  purpose,  the  white  table 
must  be  removed  farther  from  the  lens,  conformably 
to  this  general  rule,  that  the  nearer  the  object  is 
brought  to  the  convex  lens,  the  farther  does  the 
image,  where  the  white  table  ought  to  be  placed, 
retire  from  it ;  and  if  the  chamber  is  not  of  suffi- 


AND    SOLAR    MICROSCOPE. 


287 


cient  depth,  a  different  lens,  of  a  shorter  focus, 
must  be  employed. 

You  may  place,  then,  out  of  the  chamber,  before 
the  aperture  to  which  the  convex  lens  is  fitted,  any 
object  or  picture  whatever,  and  you  will  see  a  copy 
of  it  on  the  white  table  within  the  dark  chamber, 
greater  or  smaller  than  the  original,  according  as 
the  distance  of  the  image  is  greater  or  smaller;  but 
it  would  be  more  commodious,  undoubtedly,  if  the 
object  could  be  exposed  within  the  dark  chamber, 
in  order  to  its  being  moved  and  changed  at  pleasure. 
But  here  a  great  difficulty  occurs, — the  object  itself 
would  in  this  case  be  darkened,  and  consequently 
rendered  incapable  of  producing  the  effect  we  wish. 

The  thing  wanted,  then,  is  to  illuminate  the  object 
as  much  as  possible  within  the  dark  chamber,  and 
at  the  same  time  to  exclude  the  light.  I  have  found 
out  the  means  of  doing  this.  You  will  recollect 
that  I  constructed  a  machine  to  the  effect  I  am 
mentioning,  which  I  had  the  honour  of  presenting 
to  you  six  years  ago ;  and  now  you  will  easily  com- 
prehend the  structure,  and  the  principles  on  which 
it  is  founded. 

This  machine  consists  of  a  box  very  close  on  all 
sides,  nearly  of  a  figure  similar  to  Fig.  164.  The 
Fig.  164. 


288  OF    THE    MAGIC   LANTERN, 

farther  side  of  which  E  G  has  an  opening  I  K, 
in  which  are  to  be  fitted  the  objects,  portraits  or 
other  pictures,  0  P,  which  you  mean  to  represent ;  on 
the  other  side,  directly  opposite,  is  a  tube  M  N  Q  R, 
containing  a  convex  lens  M  N ;  this  tube  is  move- 
able,  for  the  purpose  of  bringing  the  lens  nearer  to 
the  object,  or  of  removing  it,  at  pleasure.  Then, 
provided  the  object  O  P  be  well  illuminated,  the 
lens  will  throw  somewhere  the  image  of  it  o  p,  and 
if  you  there  place  a  white  tablet,  you  will  see  upon 
it  a  perfect  copy  of  the  object,  so  much  the  clearer 
as  the  object  itself  is  more  illuminated. 

For  this  purpose  I  have  contrived  in  this  box  two 
side  wings,  for  the  reception  of  lamps  with  large 
wicks,  and  in  each  wing  is  placed  a  mirror  to  reflect 
the  light  of  the  lamps  on  the  objects  O  P ;  above,  at 
E  F,  is  a  chimney,  by  which  the  smoke  of  the  lamps 
passes  off.  Such  is  the  construction  of  this  ma- 
chine, within  which  the  object  O  P  may  be  very 
strongly  illuminated,  while  'the  darkness  of  the 
chamber  suffers  no  diminution.  In  order  to  the 
proper  use  of  this  machine,  attention  must  be  paid 
to  the  following  remarks. 

1.  On  sliding  inward  the  tube  M  N  Q  R,  that  is, 
bringing  the  lens  M  N  nearer  to  the  object  O  P,  the 
image  o  p  will  retire ;  the  white  tablet  must  there- 
fore be  removed  backwards,  to  receive  the  image  at 
the  just  distance ;  the  image  will  thereby  be  like- 
wise magnified,  and  you  may  go  on  to  enlarge  it  at 
pleasure,  by  pressing  the  lens  M  N  nearer  and  nearer 
to  the  object  0  P. 

2.  On  removing  the  lens  from  the  object,  the  dis- 
tance of  the  image  will  be  diminished :  the  white 
tablet  must  in  this  case  be  moved  nearer  to  the  lens, 
in  order  to  have  a  clear  and  distinct  representation ; 
but  the  image  will  be  reduced. 

3.  It  is  obvious  that  the  image  will  be  always  re- 
versed ;  but  this  inconvenience  is  easily  remedied ; 
you  have  only  to  reverse  the  object  O  P  itself,  turn- 


AND    SOLAR   MICROSCOPE.  289 

ing  it  upside  down,  and  the  image  will  be  repre- 
sented upright  on  the  white  tablet. 

4.  It  is  a  further  general  remark,  that  the  more, 
the  image  is  magnified  on  the  white  tablet,  the  less 

uminous  and  distinct  it  will  be ;  but  on  reducing 
the  image,  it  is  rendered  more  distinct  and  brilliant. 
The  reason  is  plain— the  light  proceeds  wholly  from 
the  illumination  of  the  object ;  the  greater  that  the 
space  is  over  which  it  is  diffused^  the  more  it  must 
be  weakened,  and  the  more  contracted  it  is,  the  more 
brilliant. 

5.  Accordingly,  the  more  you  wish  to  magnify  the 
representation,  the  more  you  must  strengthen  the 
illumination  of  the  object,  by  increasing  the  light 
of  the  lamps  in  the  wings  of  the  machine ;  but  for 
small  representations   a  moderate  illumination  is 
sufficient. 

The  machine  which  I  have  been  describing  is 
called  the  magic  lantern,  to  distinguish  it  from  the 
common  camera  obscura,  employed  for  representing 
distant  objects ;  its  figure,  undoubtedly,  has  procured 
it  the  name  of  lantern,  especially -as  it  is  designed 
to  contain  light ;  but  the  epithet  magic  must  have 
been  an  invention  of  its  first  proprietors,  who  wished 
to  impress  the  vulgar  with  the  idea  of  magic  or 
witchcraft.  The  ordinary  magic  lanterns,  however, 
are  not  constructed  in  this  manner,  and  serve  to 
represent  no  other  objects  but  figures  painted  on 
glass,  whereas  this  machine  may  be  applied  to  ob- 
jects of  all  sorts. 

It  may  even  be  employed  for  representing  the 
smallest  objects,  and  for  magnifying  the  representa- 
tion to  a  prodigious  size,  so  that  the  smallest  fly 
shall  appear  as  large  as  an  elephant ;  but  for  this 
purpose  the  strongest  light  that  lamps  can  give  is 
ffir  from  being  sufficient;  the  machine  must  be  dis- 
posed in  such  a  manner  that  the  objects  may  be  illu- 
minated by  the  rays  of  the  sun,  strengthened  by  a 
burning-glass ;  the  machine,  in  this  case>  changes 

VOL.  IL— B  b 


290  USE    AND   EFFECT    OF  A 

its  name,  and  is  called  the  solar  microscope.  I  shaH 
have  occasion  to  speak  of  it  more  at  large  in  the 
Sequel. 

8th  January,  1762. 


LETTER  LXXXII. 

Use  and  Effect  of  a  simple  Convex  Lens, 

WE  likewise  employ  convex  lenses  for  imme- 
diately looking  through ;  but  in  order  to  explain  their 
different  uses,  we  must  go  into  a  closer  investigation 
of  their  nature. 

Having  observed  the  focal  distance  of  such  a 
glass,  I  have  already  remarked,  that  when  the  ob- 
ject is  very  remote,  its  image  is  represented  in  the 
focus  itself;  but  on  bringing  the  object  nearer  to  the 
lens,  the  image  retires  farther  and  farther'  from  it : 
so  that  if  the  distance  of  the  object  be  equal  to  that 
of  the  focus  of  the  lens,  the  image  is  removed  to  an 
infinite  distance,  and  consequently  becomes  infinitely 
great. 

The  reason  is,  that  the  rays  OM,  OM,  Fig.  155, 

Fig.  155. 

F 


which  come  from  the  point  O,  are  refracted  by  the 
lens,  so  as  to  become  parallel  to  each  other,  as  N  F, 
N  F ;  and  as  parallel  lines  are  supposed  to  proceed 
forward  to  infinity,  and  as  the  image  is  always  in 
the  place  where  the  rays,  issuing  from  one  point 
of  the  object,  are  collected  again  after  the  refrac- 
tion ;  in  the  case  when  the  object  O  A  is  equal  to 
that  of  the  focus  of  the  lens,  the  place  of  the  image 


SIMPLE    CONVEX    LENS. 


291 


Fig.  156. 


removes  to  an  infinite  distance ;  and  as  it  is  indifferent 
whether  we  conceive  the  parallel  lines  N  F  and  N  F 
to  meet  at  an  infinite  distance  to  the  left  or  to  the 
right,  it  may  be  said  indifferently  that  the  image  is 
to  the  right  or  to  the  left  infinitely  distant,  the  effect 
being  always  the  same. 

Having  made  this  remark,  you  will  easily  judge 
what  must  be  the  place  of  the  image  when  the  ob- 
ject is  brought  still  nearer  to  the  lens. 

Let  O  P,  Fig.  156,  be  the  object, 
and  as  its  distance  O  A  from  the  con- 
vex lens  is  less  than  the  distance  of 
the  focus,  the  rays  O  M,  O  M,  which 
fall  upon  it  from  the  point  O,  are  too 
divergent  to  admit  of  the  possibility 
of  their  being  rendered  parallel  to 
each  other  by  the  refractive  power 
of  the  lens:  they  will  therefore  be 
still  divergent  after  the  refraction,  as 
marked  by  the  lines  N  F,  N  F,  though 
much  l«ss  so  than  before ;  therefore, 
if  these  lines  are  produced  backward, 
they  will  meet  somewhere  at  0,  as 
you  may  see  in  the  dotted  lines  N  0, 
N  o.  The  rays  N  F,  N  F,  will  of  con- 
sequence, after  havingpassed  through  p 
the  lens,  preserve  the  same  direction 
as  if  they  had  proceeded  from  the 
point  0,  though  they  have  not  actually  passed  through 
that  point,  as  it  is  only  in  the  lens  that  they  have 
taken  this  new  direction.  An  eye  which  receives 
these  refracted  rays  N  F,  N  F,  will  be  therefore  af- 
fected as  if  they  really  came  from  the  point  0,  and 
will  imagine  that  the  object  of  its  vision  exists  at  0. 
There  will,  however,  be  no  image  at  that  point, 
as  in  the  preceding  case.  To  no  purpose  would 
you  put  a  white  tablet  at  o ;  it  would  present  no 
picture  there  for  want  of  rays :  for  this  reason  we 
say  that  there  is  an  imaginary  image  at  0,  and  not  a 


292  USE    OF    A    SIMPLE    CONVEX    LENS. 

real  one — the  term  imaginary  being  opposed  to  that 
of  real. 

Nevertheless,  an  eye  placed  at  E  receives  the  same 
impression  as  if  the  object  O  P,  from  which  the  rays 
originally  proceed,  existed  at  o.  It  is  of  great  im- 
portance, then,  to  know,  as  in  the  preceding  cases, 
the  place  and  the  magnitude  of  this  imaginary  image 
o  p.  As  to  the  place,  it  is  sufficient  to  remark,  that 
if  the  distance  of  the  object  A  O  be  equal  to  the  dis- 
tance of  the  focus  of  the  lens,  the  image  will  be  at 
an  infinite  distance  from  it ;  and  this  is  what  the 
present  case  has  in  common  with  the  preceding ;  but 
the  nearer  the  object  is  brought  to  the  lens,  or  the 
less  that  the  distance  A  O  becomes  than  that  of  the 
focus  of  the  lens,  the  nearer  does  the  imaginary 
image  approach  to  the  lens  ;  though,  at  the  same 
time,  it  remains  always  at  a  greater  distance  from 
the  lens  than  the  object  itself. 

To  elucidate  this  by  an  example,  let  us  suppose 
that  the  focal  distance  of  the  lens  is  6  inches  ;  and 
for  the  different  distances  of  the  object,  the  an- 
nexed table  indicates  the  distance  of  the  imaginary 
image  op. 


If  the  distance  of  the  Object  \ 
A  Ois 

The  distance  of  the  imaginary 
Image  A  o  will  be 

6 
5 

4 
3 
2 
1 

Infinity 
30 
12 
6 
3 
1  and  a  fifth. 

The  rule  for  ascertaining  the  magnitude  of  this 
imaginary  image  o  p  is  easy  and  general ;  you  have 
only  to  draw  through  the  middle  of  the  lens,  marked 
C,  and  through  the  extremity  of  the  object  P,  the 
straight  line  C  P  p ;  and  where  it  meets  with  the 
line  o  p  drawn  from  o  at  right  angles  with  the  axis 


USE    OF    A    CONCAVE    LENS.  293 

of  the  lens,  you  will  have  found  the  magnitude  of 
the  imaginary  image  o  p  :  from  which  it  is  evident, 
that  this  image  is  always  greater  than  the  object 
O  P  itself,  as  many  times  as  it  is  farther  from  the 
lens  than  the  object  O  P.  It  is  likewise  evident 
that  this  image  is  not  reversed,  as  in  the  preceding 
case,  but  upright  as  the  object. 

You  will  easily  comprehend,  from  what  I  have 
said,  the  benefit  that  may  be  derived  from  lenses  of 
this  sort,  by  persons  whose  sight  is  not  adapted  to 
the  view  of  near  objects,  but  who  can  see  them  to 
more  advantage  at  a  considerable  distance.  They 
have  only  to  look  at  objects  through  a  convex  lens, 
in  order  to  see  them  as  if  they  were  very  distant. 
The  defect  of  sight  with  respect  to  near  objects 
occurs  usually  in  aged  people,  who  consequently 
make  use  of  spectacles  with  convex  glasses,  which, 
exposed  to  the  sun  produce  the  effect  of  a  burning- 
glass,  and  this  ascertains  the  focal  distance  of  every 
glass.  Some  persons  have  occasion  for  spectacles 
of  a  very  near  focus,  others  of  one  more  distant, 
according  to  the  state  of  their  sight ;  but  it  is  suffi- 
cient for  my  present  purpose  to  have  given  a  gen- 
eral idea  of  the  use  of  such  spectacles. 

12th  January,  1762. 


LETTER  LXXXIIL 

Use  and  Effect  of  a  Concave  Lens. 

You  have  seen  how  convex  glasses  assist  the  sight 
of  old  people,  by  representing  to  them  objects  as  at 
a  greater  distance  than  they  really  are ;  there  are 
eyes,  on  the  contrary,  which,  in  order  to  distinct 
vision,  require  the  objects  to  be  represented  as 
nearer ;  and  concave  glasses  procure  them  this  ad- 
vantage ;  which  leads  me  to  the  explanation  of  the 
Bb2 


294 


USE   AND   EFFECT   OF 


Fig.  157. 


effect  of  concave  lenses,  which  is  directly  the  con- 
trary of  that  of  convex  ones. 

When  the  object  O  P,  Fig.  157, 
is  very  distant,  and  its  rays  O  M, 
O  M,  fall  almost  parallel  on  the 
concave  lens  T  T ;  in  this  case, 
instead  of  becoming  convergent 
by  the  refraction  of  the  lens, 
they,  on  the  contrary,  become 
more  divergent,  pursuing  the 
direction  N  F,  N  F,  which,  pro- 
duced backward,  meet  at  the 
point  o ;  so  that  an  eye  placed, 
for  example,  at  E,  receives  these 
refracted  rays  in  the  same  man- 
ner as  if  they  proceeded  from 
the  point  0,  though  they  really 
proceed  from  the  point  O ;  for 
this  reason,  I  have  in  the  figure 
dotted  the  straight  lines  N  o. 
No. 

As  the  object  is  supposed  to 
be  infinitely  distant,  were  the 
lens  convex  the  point  o  would  be 
what  we  call  the  focus ;  but  as,  in  the  present  case, 
there  is  no  real  concurrence  of  rays,  we  call  this 
point  the  imaginary  focus  of  the  concave  lens ;  some 
authors  likewise  denominate  it  the  point  of  dispersion, 
because  the  rays,  refracted  by  the  glass,  appear  to 
be  dispersed  from  this  point. 

Concave  lenses,  then,  have  no  real  focus,  like  the 
convex,  but  only  an  imaginary  focus,  the  distance  of 
which  from  the  lens  A  o  is,  however,  denominated 
the  focal  distance  of  this  lens,  and  serves,  by  means 
of  a  rule  similar  to  that  which  is  laid  down  for  con- 
vex lenses,  to  determine  the  place  of  the  image, 
when  the  object  is  not  infinitely  distant.  Now,  this 
image  is  always  imaginary ;  whereas  in  the  case  of 
convex  lenses,  it  becomes  so  only  when  the  object  is 


A    CONCAVE    LENS.  295 

nearer  than  the  distance  of  the  focus.  Without 
entering  into  the  explanation  of  this  rule,  which 
respects  calculation  merely,  it  is  sufficient  to  re-' 
mark : — 

1.  When  the  object  O  P  is  infinitely  distant,  the 
imaginary  image  o  p  is  represented  at  the  focal  dis- 
tance of  the  concave  lens,  and  this,  too,  on  the  same 
side  with  the  object.     Nevertheless,  though  this 
image  be  imaginary,  the  eye  placed  at  E  is  quite  as 
much  affected  by  it  as  if  it  were  real,  conformably 
to  the  explanation  given  on  the  subject  of  convex 
lenses,  when  the  object  is  nearer  the  lens  than  its 
focal  distance. 

2.  On  bringing  the  object  O  P  nearer  to  the  lens, 
its  image  o  p  will  likewise  approach  nearer,  but  in 
such  a  manner  that  the  image  will  always  be  nearer 
to  the  lens  than  the  object  is ;  whereas,  in  the  case 
of  convex  lenses,  the  image  is  more  distant  from  the 
lens  than  the  object.     In  order  to  elucidate  this  more 
clearly,  let  us  suppose  the  focal  distance  of  the  con- 
cave lens  to  be  6  inches. 


If  the  Distance  of  the  Object 
0  A  is 

The  Distance  of  the  Image 
o  A  will  be 

Infinite. 
30 
12 
6 
3 
2 

6 
5 

4 
3 
2 
1  and  a  half. 

3.  By  the  same  rule  you  may  always  determine 
the  magnitude  of  the  imaginary  image  o  p.  You 
draw  from  the  middle  of  the  lens  a  straight  line,  to 
the  extremity  of  the  object  P,  which  will  pass  through 
the  extremity  p  of  the  image.  For,  since  the  line 
P  A  represents  a  ray  coming  from  the  extremity  of 
the  object,  this  same  ray  must,  after  the  refraction, 
pass  through  the  extremity  of  the  image ;  but  as 


296  USE    OF   A   CONCAVE    LENS. 

this  ray  PA  passes  through  the  middle  of  the  lens, 
it  undergoes  no  refraction  ;  therefore  it  must  itself 
pass  through  the  extremity  of  the  image,  at  the 
point  p. 

4.  This  image  is  not  reversed,  but  in  the  same 
position  with  the  object ;  and  it  may  be  laid  down 
as  a  general  rule,  that  whenever  the  image  falls  on 
the  same  side  of  the  lens  that  the  object  is,  it  is 
always  represented  upright,  whether  the  Ions  .be 
convex  or  concave;  but  when  represented  on  the 
other  side  of  the  lens,  it  is  always  reversed ;  and  this 
can  take  place  only  in  convex  lenses. 

5.  It  is  evident  therefore  that  the  images  repre- 
sented by  concave  lenses  are  always  smaller  than  the 
objects ;  the  reason  is  obvious — the  image  is  always 
nearer  than  the  object;  you  have  only  lp  look  at 
the  figure  to  be  satisfied  of  this  truth.     These  are 
the  principal  properties  to  be  remarked  respecting 
the  nature  of  concave  lenses,  and  the  manner  in  which 
objects  are  represented  by  them. 

It  is  now  easy  to  comprehend  how  concave  glasses 
may  be  rendered  essentially  serviceable  to  persons 
whose  sight  is  short.  You  are  acquainted  with  some 
who  can  neither  read  nor  write  without  bringing  the 
paper  almost  close  to  their  nose.  In  order,  therefore, 
to  their  seeing  distinctly,  the  object  must  be  brought 
very  near  to  the  organ  of  vision :  I  think  I  have  for- 
merly remarked  that  such  persons  are  denominated 
myopes.  Concave  lenses,  then,  may  be  made  of  great 
use  to  them,  for  they  represent  the  most  distant  ob- 
jects as  very  near ;  the  image  not  being  farther  from 
such  glasses  than  their  focal  distance,  which,  for  the 
most  part,  is  only  a  few  inches. 

These  images,  it  is  true,  are  much  smaller  than 
the  objects  themselves ;  but  this  by  no  means  prevents 
distinctness  of  vision.  A  small  object  near  may 
appear  greater  than  a  very  large  body  at  a  distance. 
In  fact,  the  head  of  a  pin  appears  to  the  eye  greater 


OF    MICROSCOPES    IN    GENERAL.  297 

than  a  star  in  the  heavens,  though  that  star  far  ex- 
ceeds the  earth  in  magnitude. 

Persons  whose  sight  is  short,  or  myopes,  have 
occasion,  then,  for  glasses  which  represent  objects  , 
as  nearer;  such  are  concave  lenses.  And  those 
whose  sight  is  long,  or  presbytes,  need  convex 
glasses,  which  represent  to  them  objects  at  a  greater 
distance. 

16th  January,  1762. 


LETTER  LXXXIV. 

Of  apparent  Magnitude,  of  the  Visual  Angle,  and  of 
Microscopes  in  general. 

I  HAVE  been  remarking,  that  myopes  are  obliged 
to  make  use  of  concave  glasses  to  assist  their  vision 
of  distant  objects,  and  that  presbytes  employ  convex 
glasses  in  order  to  a  more  distant  vision  of  such  as 
are  near ;  each  sight  has  a  certain  extent,  and  each 
requires  a  glass  which  shall  represent  objects  per- 
fectly. This  distance  in  the  myopes  is  very  small, 
and  in  the  presbytes  very  great ;  but  there  are  eyes 
so  happily  conformed  as  to  see  nearer  and  more 
distant  objects  equally  well. 

Nevertheless,  of  whatever  nature  any  person's 
sight  may  be,  this  distance  is  never  very  small :  there 
is  no  myope  capable  of  seeing  distinctly  at  the  dis- 
tance of  less  than  an  inch ;  you  must  have  observed, 
that  when  the  object  is  brought  too  close  to  the  eye, 
it  has  a  very  confused  appearance  ;  this  depends  on 
the  structure  of  the  organ,  which  is  such  in  the  hu- 
man species  as  not  to  admit  of  their  seeing  objects 
very  near.  To  insects,  on  the  contrary,  very  distant 
objects  are  invisible,  while  they  easily  see  such  as 
are  nearer.  I  do  not  believe  that  a  fly  is  capable  of 
seeing  the  stars,  because  it  can  see  extremely  well 
at  the  distance  of  the  tenth  part  of  an  inch,  a  dis* 


298  OF    MICROSCOPES    IN    GENERAL. 

tance  at  which  the  human  eye  can  distinguish  abso- 
lutely nothing.  This  leads  me  to  an  explanation  of 
the  microscope,  which  represents  to  us  the  smallest 
object  as  if  it  were  very  great. 

In  order  to  convey  a  just  idea  of  it,  I  must  entreat 
you  carefully  to  distinguish  between  the  apparent 
and  the  real  magnitude  of  every  object.  Real  mag- 
nitude constitutes  the  object  of  geometry,  and  is  in- 
variable as  long  as  the  body  remains  in  the  same  state. 
But  apparent  magnitude  admits  of  infinite  variety, 
though  the  body  may  remain  always  the  same.  The 
stars,  accordingly,  appear  to  us  extremely  small, 
though  their  real  magnitude  is  prodigious,  because 
we  are  at  an  immense  distance  from  them.  Were 
it  possible  to  approach  them,  they  would  appear 
greater;  from  which  you  will  conclude  that  the  ap- 
parent magnitude  depends  on  the  angle  formed  in  our 
eyes  by  the  rays  which  proceed  from  the  extremities 
of  the  object. 

Let  P  O  Q,  Fig.  158,  be  the  object  of 
vision,  which,  if  the  eye  were  placed 
at  A,  would  appear  under  the  angle 
P  A  Q,  called  the  visual  angle,  and 
which  indicates  to  us  the  apparent 
magnitude  of  the  object ;  it  is  evident, 
on  inspecting  the  figure,  that  the  far- 
ther the  eye  withdraws  from  the  ob- 
ject, the  smaller  this  angle  becomes, 
and  that  it  is  possible  for  the  greatest 
bodies  to  appear  to  us  under  a  very 
small  visual  angle,  provided  our  dis- 
tance from  them  be  very  great,  as  is 
the  case  with  the  stars.  But  when  the 
eye  approaches  nearer  to  the  object, 
and  looks  at  it  from  B,  it  will  appear 
under  the  visual  angle  P  B  Q,  which 
is  evidently  greater  than  P  A  Q.  Let  the  eye  advance 
still  forward  to  C,  and  the  visual  angle  P  C  Q  is  still 
greater.  Further,  the  eye  being  placed  at  D,  the 


OF   MICROSCOPES   IN   GENERAL.  299 

visual  angle  will  be  P  D  Q ;  and  on  advancing  for- 
ward to  E,  the  visual  angle  will  be  P  E  Q,  always 
greater  and  greater.     The  nearer,  therefore,  the  eye 
approaches  to  the  object,  the  more  the  visual  angle 
increases,  and  consequently  likewise  the  apparent 
magnitude.     However  small  the  object  may  be,  it  is 
possible,  therefore,  to  increase  its  apparent  magnitude 
at  pleasure ;  you  have  only  to  bring  it  so  near  the 
eye  as  is  necessary  to  form  such  a  visual  angle.     A 
fly  near  enough  to  the  eye  may,  of  consequence, 
appear  under  an  angle  as  great  as  an  elephan-t  at 
the  distance  of  ten  feet.     In  a  comparison  of  this 
sort,  we  must  take  into  the  account  the  distance  at 
which  we  suppose  the  elephant  to  be  viewed ;  un- 
less this  is  done,  we  affirm  absolutely  nothing ;  for 
an  elephant  appears  great  only  when  we  are  not 
very  far  from  it ;  at  the  distance  of  a  mile,  it  would 
be  impossible,  perhaps,  to  distingush  an  elephant 
from  a  pig ;  and,  transported  to  the  moon,  he  would 
become  absolutely  invisible ;    and  I   might   affirm 
with  truth,  that  a  fly  appeared  to  me  greater  than 
an  elephant,  if  the  latter  was  removed  to  a  very 
considerable  distance.      Accordingly,  if  we  would 
express   ourselves   with   precision,  we    must   not 
speak  of  the  apparent  magnitude  of  a  body,  without 
taking  distance  likewise  into  the  account,  as  the 
same  body  may  appear  very  great  or  very  small  ac- 
cording as  its  distance  is  greater  or  less.     It  is  very 
easy,  then,  to  see  the  smallest  bodies  under  very 
great  visual  angles ;  they  need  only  to  be  placed 
very  close  to  the  eye. 

This  expedient  may  be  well  enough  adapted  to  a 
fly,  but  the  human  eye  could  see  nothing  at  too 
small  a  distance,  however  short  the  sight  may  be ; 
besides,  persons  of  the  best  sight  would  wish  to  see 
likewise  the  smallest  objects  extremely  magnified. 
The  thing  required,  then,  is  to  find  the  means  of  en- 
abling us  to  vi'ew  an  object  distinctly,  notwithstand- 
ing its  great  proximity  to  the  eye.  Convex  lenses 


300  OBJECTS   VIEWED   THROUGH 

render  us  this  service,  by  removing  the  image  of  ob- 
jects which  are  too  near. 

Let  a  very  small  convex  lens  M  N  be  employed, 
Fig.  159,  the  focal  distance  of  which  shall  be  half  an 
Fig.  159. 


inch ;  if  you  place  before  it  a  small  object  O  P,  at  a 
distance  somewhat  less  than  half  an  inch,  the  lens 
will  represent  the  image  of  it  o  p,  as  far  off  as  could 
be  wished.  On  placing  the  eye,  then,  behind  the 
lens,  the  object  will  be  seen  as  if  it  were  at  0,  and  at 
a  sufficient  distance,  as  if  its  magnitude  were  o  p : 
as  the  eye  is  supposed  very  near  the  lens,  the  visual 
angle  will  be  p  I  o,  that  is,  the  same  as  P,  t  O,  under 
which  the  naked  eye  would  see  the  object  O  P  in 
that  proximity ;  but  the  vision  is  become  distinct  by 
means  of  the  lens  :  such  is  the  principle  on  which 
microscopes  are  constructed. 
IQth  January,  1762. 


LETTER  LXXXV. 

Estimation  of  the  Magnitude  of  Objects  viewed  through 
the  Microscope. 

WHEN  several  persons  view  the  same  object 
through  a  microscope,  the  foot  of  a  fiy,  for  example, 
they  all  agree  that  they  see  it  greatly  magnified,  but 
their  judgment  respecting  the  real  magnitude  will 
Vary ;  one  will  say,  it  appears  to  him  as  large  as  that 
of  a  horse ;  another,  as  that  of  a  goat ;  a  third,  as 
that  of  a  cat.  No  one  then  advances  any  thing  posi- 
tive on  the  subject,  unless  he  adds  at  what  distance 
he  views  the  feet  of  the  horse,  the  goat,  or  the  cat. 


THE    MICROSCOPE.  301 

They  all  mean,  therefore,  without  expressing  it,  a 
certain  distance,  which  is  undoubtedly  different ;  con- 
sequently, there  is  no  reason  to  be  surprised  at  the 
variety  of  the  judgments  which  they  pronounce,  as 
the  foot  of  a  horse  viewed  at  a  distance,  may  very 
well  appear  no  bigger  than  that  of  a  cat  viewed  near 
to  the  eye.  Accordingly,  when  the  question  is  to 
be  decided,  How  much  does  the  microscope  mag- 
nify an  object  1  we  must  accustom  ourselves  to  a 
more  accurate  mode  of  expression,  and  particularly 
to  specify  the  distance,  in  the  comparison  which  we 
mean  to  institute. 

It  is  improper,  therefore,  to  compare  the  appear- 
ances presented  to  us  by  the  microscope  with  objects 
of  another  nature,  which  we  are  accustomed  to  view 
sometimes  near  and  sometimes  at  a  distance.  The 
most  certain  method  of  regulating  this  estimation 
seems  to  be  that  which  is  actually  employed  by  au- 
thors who  treat  of  the  microscope.  They  compare 
a  small  object  viewed  through  the  microscope  with 
the  appearance  which  it  would  present  to  the  naked 
eye  on  being  removed  to  a  certain  distance;  and 
they  have  determined,  that  in  order  to  contemplate 
such  a  small  object  to  advantage  by  the  naked  eye, 
it  ought  to  be  placed  at  the  distance  of  eight  inches, 
which  is  the  standard  for  good  eyes,  for  a  short- 
sighted person  would  bring  it  closer  to  the  eye,  and 
one  far-sighted  would  remove  it.  But  this  difference 
does  not  affect  the  reasoning,  provided  the  regulating 
distance  be  settled ;  and  no  reason  can  be  assigned 
for  fixing  on  any  other  distance  than  that  of  eight 
inches,  the  distance  received  by  all  authors  who 
have  treated  of  the  subject.  Thus,  when  it  is  said* 
that  a  microscope  magnifies  the  object  a  hundred 
times,  you  are  to  understand  that,  with  the  assist- 
ance of  such  a  microscope,  objects  appear  a  hundred 
times  greater  than  if  you  viewed  them  at  the  dis- 
tance of  eight  inches ;  and  thus  you  will  form  a  just 
idea  of  the  effect  of  a  microscope. 

VOL.  II.— €  c 


802  OBJECTS    VIEWED    THROUGH 

In  general,  a  microscope  magnifies  as  many  times 
as  an  object  appears  larger  than  if  it  were  viewed 
without  the  aid  of  the  glass  at  the  distance  of  eight 
inches.  You  will  readily  admit  that  the  effect  is 
surprising,  if  an  object  is  made  to  appear  even  a 
hundred  times  greater  than  it  would  to  the  naked 
eye  at  the  distance  of  eight  inches :  but  it  has  been 
carried  much  farther ;  and  microscopes  have  been 
constructed  which  magnify  five  hundred  times — a 
thing  almost  incredible.  In  such  a  case  it  might  be 
with  truth  affirmed  that  the  leg  of  a  fly  appears 
greater  than  that  of  an  elephant.  Nay,  I  have  full 
conviction  that  it  is  possible  to  construct  micro- 
scopes capable  of  magnifying  one  thousand,  or  even 
two  thousand  times,  which  would  undoubtedly  lead 
to  the  discovery  of  many  things  hitherto  unknown. 

But  when  it  is  affirmed  that  an  object  p  16 
appears  through  the  microscope  a  hundred  ' 
times  greater  than  when  viewed  at  the  dis-» 
tance  of  eight  inches,  it  is  to  be  under- 
stood that  the  object  is  magnified  as  much 
in  length  as  in  breadth  and  depth,  so  that 
each  of  these  dimensions  appears  a  hundred 
times  greater.  You  have  only,  then,  to 
conceive  at  the  distance  of  eight  inches 
another  object  similar  to  the  first,  but  whose 
length  is  a  hundred  times  greater,  as  well 
as  its  breadth  and  depth,  and  such  will  be 
the  image  viewed  through  the  microscope. 
Now,  if  the  length,  the  breadth,  and  depth 
of  an  object  be  a  hundred  times  greater 
fthan  those  of  another,  you  will  easily  per- 
'ceive  that  the  whole  extent  will  be  much 
more  than  a  hundred  times  greater.  In 
order  to  put  this  in  the  clearest  light,  let 
us  conceive  two  parallelograms  A  B  C  D, 
and  E  F  G  H,  Fig.  160,  of  the  same  breadth,  but  that 
the  length  of  the  first,  A  B,  shall  be  five  times  greater 


m 


THE    MICROSCOPE.  303 

than  the  length  of  the  other,  E  F ;  it  is  evident  that 
the  area,  or  space  contained  in  the  first,  is  five 
times  greater  than  that  contained  in  the  other,  as 
in  fact  this  last  is  contained  five  times  in  the  first. 
To  render,  then,  the  parallelogram  A  D  five  times 
greater  than  the  parallelogram  E  H,  it  is  sufficient 
that  its  length  A  B  be  five  times  greater,  the  breadth 
being  the  same ;  and  if,  besides,  the  breadth  were 
likewise  five  times  greater,  it  would  become  five 
times  greater  still,  ttfat  is,  five  times  five  times,  or 
twenty-five  times  greater.  Thus,  of  two  surfaces, 
if  the  one  be  five  times  longer  and  five  times 
broader  than  the  other,  it  is  in  fact  twenty-five  times 
greater. 

If  we  take,  further,  the  height  or  depth  into  the 
account,  the  increase  will  be  still  greater.  Conceive 
two  apartments,  the  one  of  which  is  five  times 
longer,  five  times  broader,  and  five  times  higher 
than  the  other ;  its  contents  will  be  five  times  25 
times,  that  is,  125  times  greater.  When,  therefore, 
it  is  said  that  a  microscope  magnifies  100  times,  as 
this  is  to  be  understood,  not  only  of  length,  but  of 
breadth,  and  depth,  or  thickness,  that  is,  of  three 
dimensions,  the  whole  extent  of  the  object  will  be 
increased  100  times  100  times  100  times;  now  100 
times  100  make  10,000,  which  taken  again  100  times 
make  1,000,000  ;  thus,  when  a  microscope  magnifies 
100  times,  the  whole  extent  of  the  object  is  repre- 
sented 1,000,000  times  greater.  We  satisfy  our- 
selves, however,  with  saying  that  the  microscope 
magnifies  100  times ;  but  it  is  to  be  understood  that 
all  the  three  dimensions,  namely,  length,  breadth, 
and  depth,  are  represented  100  times  greater.  If, 
then,  a  microscope  should  magnify  1000  times,  the 
whole  extent  of  the  object  would  become  1000 
times  1000  times  1000  times  greater,  which  makes 
1,000,000,000,  or  a  thousand  millions :  a  most  aston- 
ishing effect!  This  remark  is  necessary  to  the 


304  PLAN    OF    SIMPLE    MICROSCOPES. 

formation  of  a  just  idea  of  what  is  said  respecting 
the  power  of  microscopes.* 
23d  January,  1762. 


LETTER  LXXXVI. 

Fundamental  Propositionfor  the  Construction  of  Simple 
Microscopes.     Plan  of  some  Simple  Microscopes. 

HAVING  explained  in  what  manner  we  are  enabled 
to  judge  of  the  power  of  microscopes,  it  will  be  easy 
to  unfold  the  fundamental  principle  for  the  con- 
struction of  simple  microscopes.  And  here  it  may 
be  necessary  to  remark,  that  there  are  two  kinds 
of  microscopes ;  some  consisting  of  a  single  lens, 
others  of  two  or  more,  named,  accordingly,  simple 
or  compound  microscopes,  and  which  require  par- 
ticular elucidations.  I  shall  confine  myself  at  pres- 
ent to  the  simple  microscope,  which  consists  of  a 
single  convex  lens,  the  effect  of  which  is  determined 
by  the  following  proposition :  A  simple  microscope 
magnifies  as  many  times  as  its  focal  distance  is  nearer 
than  eight  inches.  The  demonstration  follows. 

Let  M  N,  Fig.  161,  be  a  con-  jvg-.  161. 

vex  lens,  whose  focal  distance,  p^ 
at  which  the  object  0  P  must  \ 

be  placed  nearly,  in  order  that  o| ^ 

the  eye  may  see  it  distinctly, 

shall  be  C  O  ;  this  object  will 

be  perceived  under  the  angle 

OOP.     But  if  it  be  viewed  at  the  distance  of  eight 

inches,  it  would  appear  under  an  angle  as  many  times 

smaller  as  the  distance  of  eight  inches  surpasses 

*  As  it  is  in  reality  only  the  surface  of  bodies  that  is  presented  to  the 
eye,  it  may  be  questioned  whether  the  magnifying  power  of  a  micro- 
scope ought  to  be  estimated  at  a  higher  rate  than  that  of  the  square : 
thus,  if  it  magnify  100  times  in  length,  the  object  will  appear  10,000 
times  greater  tb.au  to  the  naked  eye. — Am.  Ed. 


PLAN    OF    SIMPLE    MICROSCOPES.  305 

the  distance  C  O:  the  object  will  appear,  therefore, 
as  many  times  greater  than  if  it  were  viewed  at  the 
distance  of  eight  inches.  Now,  in  conformity  to 
the  rule  already  established,  a  microscope  magnifies 
as  many  times  as  it  presents  the  object  greater  than 
if  we  viewed  it  at  the  distance  of  eight  inches. 
Consequently,  a  microscope  magnifies  as  many 
times  as  its  focal  distance  is  less  than  eight  inches. 
A  lens,  therefore,  whose  focal  distance  is  an  inch 
will  magnify  precisely  eight  times ;  and  a  lens  whose 
focal  distance  is  only  half  an  inch  will  magnify  six- 
teen times.  The  inch  is  divided  into  twelve  parts, 
called  lines ;  half  an  inch,  accordingly,  contains  six 
lines :  hence  it  would  be  easy  to  determine  how 
many  times  every  lens,  whose  focal  distance  is  given 
in  lines,  must  magnify ;  according  to  the  following 
table  :— 

Focal  distance  of  the  lens  in  lines. 

12,  8,     6,    4,     3,     2,    1,      4    lines, 
magnifies    8,  12,  16,  24,  32,  48,  96,  192  times. 

Thus  a  convex  lens  whose  focal  distance  is  one 
line  magnifies  ninety-six  times;  and  if  the  distance 
be  half  a  line,  the  microscope  will  magnify  one  hun- 
dred and  ninety-two,  that  is,  near  two  hundred  times. 
Were  greater  effect  still  to  be  desired,  lenses  must 
be  constructed  of  a  still  smaller  focus.*  Now,  it 
has  been  already  remarked,  that  in  order  to  con- 
struct a  lens  of  any  certain  given  focus,  it  is  only 
necessary  to  make  the  radius  of  each  face  equal  to 
that  focal  distance,  so  that  the  lens  may  become 
equally  convex  on  both  sides.  I  now  proceed,  then, 
to  place  before  you,  Fig.  162,  the  form  of  some  of 
these  lenses  or  microscopes : — 

No.  I.  The  focal  distance  of  this  lens  A  O  is  one 
inch,  or  twelve  lines.  This  microscope,  therefore, 
magnifies  eight  times. 

*  Lenses  have  been  ground  and  polished  having  only  a  focal  length  of 
one-fiftieth  of  an  inch,  consequently  their  magnifying  power  is  400 
times.  -Ed. 

Cc2 


306  PLAN    OF    SIMPLE    MICROSCOPES. 

No.  II.  The  focal  distance  of  the     Fig.  162. 
lens  M  N  is  eight  lines.     This  micro-   p    j     M<*^ 
scope  magnifies  twelve  times.  i — '. — -rfl  jb- 

No.  III.  The  focal  distance  of  the  &  ^ 

lens  M  N  is  six  lines.      This  micro-       r  Ji  y**^ 
scope  magnifies  sixteen  times.  o     ^v^ 

No.  IV.  The  focal  distance  of  this 
lens  is  four  lines ;  and  such  a  micro-         'o~l^_ 
scope  magnifies  twenty-four  times. 

No.  V.  The  focal  distance  here  is 
three  lines.  This  microscope  magni- 
fies thirty-two  times.  H)  ;fcp 

No.  VI.  The  focal  distance  here  is  ^^ 

two   lines.     This  microscope  magni- 
fies forty-eight  times.  ^^ 

No.  VII.  The  focal  distance  of  this 
lens  is  only  one  line ;  and  such  a  microscope  mag- 
nifies ninety-six  times. 

It  is  possible  to  construct  microscopes  still  much 
smaller.  They  are  actually  executed,  and  much 
more  considerable  effects  are  produced ;  whence  it 
must  be  carefully  remarked,  that  the  distance  of  the 
object  from  the  glass  becomes  smaller  and  smaller, 
as  it  must  be  nearly  equal  to  the  focal  distance  of 
the  lens.  I  say  nearly,  as  every  eye  brings  the  glass 
closer  to  it  somewhat  more  or  less,  according  to  its 
formation ;  the  short-sighted  apply  it  closer,  the  far- 
sighted  less  so.  You  perceive,  then,  that  the  effect 
is  greater  as  the  microscope  or  lens  becomes  smaller, 
and  the  closer  likewise  the  object  must  be  applied : 
this  is  a  very  great  inconvenience,  for,  on  the  one 
hand,  it  is  troublesome  to  look  through  a  glass  so 
very  small ;  and,  on  the  other,  because  the  object 
must  be  placed  so  near  the  eye.  Attempts  have 
been  made  to  remedy  this  inconvenience  by  a  proper 
mounting,  which  may  facilitate  the  use  of  it ;  but  the 
vision  of  the  object  is  considerably  disturbed  as  soon 
as  the  distance  of  it  undergoes  the  slightest  change : 
and  as  in  the  case  of  a  very  small  lens  the  object  must 


DEFECTS    OF    THE    SIMPLE    MICROSCOPE.       307 

almost  touch  it,  whenever  the  surface  of  the  object 
is  in  the  least  degree  unequal,  it  is  seen  but  —         o 
confusedly.    For,  while  the  eminences  are 
viewed  at  the  just  distance,  the  cavities, 
being  too  far  removed,  must  be  seen  very 
confusedly.     This  renders  it  necessary  to 
lay  aside  simple  microscopes  when  we 
wish  to  magnify  very  considerably,  and  to 
have  recourse  to  the  compound  micro- 
scope. 

26ik  January,  1762. 


LETTER  LXXXVII. 

Limits  and  Defects  of  the  Simple  Microscope. 

You  have  now  seen  how  simple  micro- 
scopes may  be  constructed,  which  shall 
magnify  as  many  times  as  may  be  desired  ; 
you  have  only  to  measure  off  a  straight  line 
of  eight  inches,  like  that  which  I  have 
marked  A  B,*  Fig.  163,  which  contains 
precisely  eight  inches  of  the  Rhenish  foot, 
which  is  the  standard  all  over  Germany. 
This  line  A  B  must  then  be  subdivided 
into  as  many  equal  parts  as  correspond  to 
the  number  of  times  you  wish  to  magnify 
the  object  proposed,  and  one  of  these 
parts  will  give  the  focal  distance  of  the 
lens  that  is  requisite.  Thus,  if  you  wish 
to  magnify  a  hundred  times,  you  must 
take  the  hundredth  part  of  the  line  A  B; 
consequently,  you  must  construct  a  lens 
whose  focal  distance  shall  be  precisely 
equal  to  that  part  A  i,  which  will  give,  at 
the  same  time,  the  radius  of  the  surfaces 

*  It  being  impossible  here  to  insert  a  straight  line  of  eight  inches,  one 
of  half  that  length  is  employed,  for  the  purpo.se  of  illustration. 


308  DEFECTS    OF 

of  the  lens  represented  in  No.  VII.  of  the  preceding 
figure.  Hence  it  is  evident,  that  the  greater  the 
effect  we  mean  to  produce,  the  smaller  must  be  the 
lens,  as  well  as  the  focal  distance  at  which  the  object 
O  P  must  be  placed  before  the  lens,  while  the  eye  is 
applied  behind  it :  and  if  the  lens  were  to  be  made 
twice  smaller  than  what  I  have  now  described,  in 
order  to  magnify  two  hundred  times,  it  would  be- 
come so  minute  as  almost  to  require  a  microscope 
to  see  the  lens  itself;  besides,  it  would  be  neces- 
sary to  approach  so  close  as  almost  to  touch  the 
lens,  which,  as  I  have  already  observed,  would  be 
very  inconvenient.  The  effect  of  the  microscope, 
therefore,  could  hardly  be  carried  beyond  two  hun- 
dred times ;  which  is  by  no  means  sufficient  for  the 
investigation  of  many  of  the  minuter  productions 
of  nature.  The  purest  water  contains  small  ani- 
malcules, which,  though  magnified  two  hundred 
times,  still  appear  no  bigger  than  fleas ;  and  a  mi- 
croscope which  should  magnify  20,000  times  would 
be  necessary  to  magnify  their  appearance  to  the  size 
of  a  rat;  and  we  are  far  from  reaching  this  degree,  even 
with  the  assistance  of  the  compound  microscope.* 

But  besides  the  inconveniences  attending  the  use 
of  simple  microscopes  which  have  been  already 
pointed  out,  all  those  who  employ  them  with  a  view 
to  very  great  effect  complain  of  another  consider- 
able defect;  it  is  this — the  more  that  objects  are 
magnified,  the  more  obscure  they  appear ;  they  seem 
as  if  viewed  in  a  very  faint  light  or  by  moonlight,  so 
that  you  can  hardly  distinguish  any  thing  clearly. 
You  will  not  be  surprised  at  this,  when  you  recol- 
lect that  the  light  of  the  full  moon  is  more  than 
two  hundred  thousand  times  fainter  than  that  of  the 
sun. 

It  is  of  much  importance,  therefore,  to  explain 

*  It  is  not  probable  that  water  perfectly  pure  contains  any  animal- 
cnlae, — that  is,  water  prepared  by  the  slow  and  careful  distillation  of  clear 
tresh  rain-water,  and  preserved  in  close  vessels. — Am.  Ed. 


THE    SIMPLE    MICROSCOPE.  309 

whence  this  diminution  of  light  proceeds.  We  can 
easily  comprehend,  that  if  the  rays  which  proceed 
from  a  very  small  object  must  represent  it  to  us  as 
if  it  were  much  larger,  this  small  quantity  of  light 
would  not  be  sufficient.  But  however  well  founded 
this  reasoning  may  appear,  it  wants  solidity,  and 
throws  only  a  false  light  on  the  question.  For  if 
the  lens,  as  it  proceeded  in  magnifying,  necessarily 
produced  a  diminution  of  clearness,  this  must  like- 
wise be  perceptible  in  the  smallest  effects,  even 
supposing  it  were  not  to  so  high  a  degree  ;  but  you 
may  magnify  up  to  fifty  times,  without  perceiving 
the  least  apparent  diminution  of  light,  which,  how- 
ever, ought  to  be  fifty  times  fainter,  if  the  reasons 
adduced  were  just.  We  must  look  elsewhere,  then, 
for  the  cause  of  this  phenomenon,' and  even  resort 
to  the  first  principles  of  vision. 

I  must  entreat  you,  then,  to  recollect  what  I  have 
already  suggested  respecting  the  use  ot  the  pupil,  or 
that  black  aperture  which  we  see  in  the  eye  at  the 
middle  of  the  iris.  It  is  through  this  aperture  that 
the  rays  of  light  are  admitted  into  the  eye  ;  accord- 
ingly, the  larger  this  aperture  is,  the  more  rays  are 
admitted.  We  must  here  consider  two  cases  in. 
which  objects  are  very  luminous  and  brilliant,  and 
in  which  they  are  illuminated  by  only  a  very  faint 
light.  In  the  first,  the  pupil  contracts  of  itself,  with- 
out any  act  of  the  will ;  and  the  Creator  has  bestowed 
on  it  this  faculty  in  order  to  preserve  the  interior  of 
the  eye  from  the  too  dazzling  effect  of  light,  which 
would  infallibly  injure  the  nerves.  Whenever,  there- 
fore, we  are  exposed  to  a  very  powerful  light,  we 
observe  that  the  pupil  of  every  eye  contracts,  to 
prevent  the  admission  of  any  more  rays  into  the  eye 
than  are  necessary  to  paint  in  it  an  image  sufficiently 
luminous.  But  the  contrary  takes  place  when  we 
are  in  the  dark;  the  pupil  in  that  case  expands,  to 
admit  the  light  in  a  greater  quantity.  This  change 
is  easily  perceptible  every  time  we  pass  from  a  dark 


310       DEFECTS    OF    THE    SIMPLE    MICROSCOPE. 

to  a  luminous  situation.  With  respect  to  the  subject 
before  us,  1  confine  myself  to  this  circumstance,  that 
the  more  rays  of  light  are  admitted  into  the  eye,  the 
more  luminous  will  be  the  image  transmitted  to  the 
retina ;  and  reciprocally,  the  smaller  the  quantity  of 
rays  which  enter  the  eye,  the  fainter  does  the  image 
become,  and,  consequently,  the  more  obscure  does 
it  appear.  It  may  happen,  that  though  the  pupil  is 
abundantly  expanded,  a  few  rays  only  shall  be  ad- 
mitted into  the  eye.  You  have  only  to  prick  a  little 
hole  in  a  card  with  a  pin,  and  look  at  an  object 
through  it ;  and  then,  however  strongly  illuminated 
by  the  sun,  the  object  will  appear  dark  in  propor- 
tion as?  the  aperture  is  small ;  nay,  it  is  possible  to 
look  at  the  sun  itself,  employing  this  precaution. 
The  reason  is  obvious,  a  few  rays  only  are  admitted 
into  the  eye  ;  however  expanded  the  pupil  may  be, 
the  pin-hole  in  the  card  determines  the  quantity  of 
light  which  enters  the  eye,  and  not  the  pupil,  which 
usually  performs  that  function. 

The  same  thing  takes  place  in  the  microscopes 
which  magnify  very  much ;  for  when  the  lens  is  ex- 
tremely small,  a  very  few  rays  only  are  transmitted, 
asm  n,  Fig.  165,  which  being  smaller  than  pig.  155. 
the  aperture  of  the  pupil,  make  the  object 
appear  so  much  more  obscure  ;  hence  it  is 
evident  that  this  diminution  of  light  takes 
place  only  when  the  lens  M  N,  or  rather  its  open, 
part,  is  smaller  than  the  pupil.  If  it  were  possible 
to  produce  a  great  magnifying  effect,  by  means  of  a 
greater  lens,  this  obscurity  would  not  take  place ; 
and  this  is  the  true  solution  of  the  question.  In 
order  to  remedy  this  inconvenience  in  the  great 
effects  of  the  microscope,  care  is  taken  to  illumi- 
nate the  object  as  strongly  as  possible,  to  give  greater 
force  to  the  few  rays  which  are  conveyed  into  the 
eye.  To  this  effect  objects  are  illuminated  by  the 
sun  itself;  mirrors  likev/ise  are  employed,  which 
reflect  on  them  the  light  of  the  sun.  These  are 


ON   TELESCOPES.  311 

nearly  all  the  circumstances  to  be  considered  re- 
specting the  simple  microscope,  and  by  these  you 
will  easily  form  a  judgment  of  the  effect  of  all  those 
which  you  may  have  occasion  to  inspect.* 
3CM  January,  1762. 


LETTER  LXXXVIII. 

On  Telescopes,  and  their  Effect. 

BEFORE  I  proceed  to  explain  the  construction  of 
compound  microscopes,  a  digression  respecting  the 
telescope  may  perhaps  be  acceptable.  These  two 
instruments  have  a  very  intimate  connexion;  the 
one  greatly  assists  the  elucidation  of  the  other.  As 
microscopes  serve  to  aid  us  in  contemplating  nearer 
objects,  by  representing  them  under  a  much  greater 
angle  than  when  viewed  at  a  certain  distance,  say 
eight  inches ;  so  the  telescope  is  employed  to  assist 
our  observation  of  very  distant  objects,  by  repre- 
senting them  under  a  greater  angle  than  that  which 
they  present  to  the  naked  eye.  Instruments  of  this 
sort  are  known  by  several  names,  according  to  their 
size  and  use  ;  but  they  must  be  carefully  distinguished 
from  the  glasses  used  by  aged  persons  to  relieve  the 
decay  of  sight. 

A  telescope  magnifies  as  many  times  as  it  repre- 
sents objects  under  an  angle  greater  than  is  pre- 
sented to  the  naked  eye.  The  moon,  for  example, 
appears  to  the  naked  eye  under  an  angle  of  half  a 
degree ;  consequently,  a  telescope  magnifies  100  times 
when  it  represents  the  moon  under  an  angle  of  fifty 
degrees,  which  is  100  times  greater  than  half  a  de- 

*  For  an  account  of  various  improvements  on  the  single  microscope, 
the  reader  is  referred  to  the  article  Optics,  in  the  Edinburgh  Encyclopaedia, 
vol.  xv.  p.  631,  and  Ferguson's  Lectures,  vol.  ii.  p.  294.— Ed. 

For  still  later  improve/rents,  see  a  paper  by  Dr.  Roget,  in  Phil, 
Transactions,  for  May,  1830.— Am.  Ed. 


312  ON    TELESCOPES, 

gree.  If  it  magnified  200  times,  it  would  represent 
the  moon  under  an  angle  of  one  hundred  degrees ; 
and  the  moon  would  in  that  case  appear  to  fill  more 
than  half  of  the  visible  heavens,  whose  whole  extent 
is  only  180  degrees.* 

In  common  language,  we  say  that  the  telescope 
brings  the  object  nearer  to  us.  This  is  a  very  equi- 
vocal mode  of  expression,  and  admits  of  two  different 
significations.  The  one,  that  on  looking  through  a 
telescope,  we  consider  the  object  as  many  times 
nearer  as  it  is  magnified.  But  I  have  already  re- 
marked, that  it  is  impossible  to  know  the  distance  of 
objects  but  by  actual  measurement,  and  that  such 
measurement  can  be  applied  only  to  objects  not 
greatly  remote  ;  when,  therefore,  they  are  so  remote 
as  is  here  supposed,  the  estimation  of  distance  might 
greatly  mislead  us.  The  other  signification,  which 
conveys  the  idea  that  telescopes  represent  objects  as 
great  as  they  would  appear  if  we  approached  nearer 
to  them,  is  more  conformable  to  truth.  You  know 
that  the  nearer  we  come  to  any  object,  the  greater 
becomes  the  angle  under  which  it  appears;  this 
explanation,  accordingly,  reverts  to  that  with  which 
I  set  out.  When,  however,  we  look  at  well-known 
objects,  say  men,  at  a  great  distance,  and  view  them 
through  a  telescope  under  a  much  greater  angle,  we 
are  led  to  imagine  such  men  to  be  a  great  deal  nearer, 
as  in  that  case  we  would,  in  effect,  see  them  under 
an  angle  so  much  greater.  But  in  examining  ob- 
jects less  approachable,  such  as  the  sun  and  moon, 
no  measurement  of  distance  can  take  place.  This 
case  is  entirely  different  from  that  which  I  have  for- 
merly submitted  to  you,  that  of  a  concave  lens,  em- 

*  The  magnifying  power  is  ascertained  by  measuring  the  aperture 
of  the  object-glass,  and  that  of  the  little  image  of  it  which  is  formed  at  the 
end  of  the  eye-piece ;  the  proportion  between  these  will  give  the  ratio  of 
the  magnifying  power. 

When  single  lenses  are  used,  the  power  of  a  glass  is  readily  discovered 
by  dividing  the  focal  length  of  the  object-glass  bv  that  of  the  eye-glass. — 
Am.  Ed. 


AND    THEIR   EFFECT.  313 

by  near-sighted  persons,  which  represents 
the  images  of  objects  at  a  very  small  distance.  The 
concave  lens  which  I  use,  for  example,  represents  to 
me  the  images  of  all  remote  objects  at  the  distance 
of  four  inches ;  it  is  impossible  for  me,  however,  to 
imagine  that  the  sun,  moon,  and  stars  are  so  near : 
accordingly,  we  do  not  conclude  that  objects  are 
where  their  images  are  found  represented  by  glasses ; 
we  believe  this  as  little  as  we  do  the  existence  of 
objects  in  our  eyes,  though  their  images  are  painted 
there.  You  will  please  to  recollect,  that  the  esti- 
mation of  the  real  distance  and  real  magnitude  of  ob- 
jects depends  on  particular  circumstances. 

The  principal  purpose  of  telescopes,  then,  is  to 
increase,  or  multiply,  the  angle  under  which  objects 
appear  to  the  naked  eye ;  and  the  principal  division  of 
telescopes  is  estimated  by  the  effect  which  they  pro- 
cure. Accordingly,  we  say  such  a  telescope  magni- 
fies five,  another  ten,  another  twenty,  another  thirty 
times,  and  so  on.  And  here  I  remark,  that  pocket- 
glasses  rarely  magnify  beyond  ten  times;  but  the 
usual  telescopes  employed  for  examining  very  dis- 
tant terrestrial  objects  magnify  from  twenty  to  thirty 
times,  and  their  length  amounts  to  six  feet  or  more. 
A  similar  effect,  though  very  considerable  with 
regard  to  terrestrial  objects,  is  a  mere  nothing  with 
respect  to  the  heavenly  bodies,  which  require  an 
effect  inconceivably  greater.  We  have,  accordingly, 
astronomical  telescopes  which  magnify  from  50 
to  200  times ;  and  it  would  be  difficult  to  go  further, 
as,  according  to  the  usual  mode  of  constructing 
them,  the  greater  the  effect  is  the  longer  they 
become.  A  telescope  that  shall  magnify  100  times 
must  be  at  least  30  feet  long :  and  one  of  100  feet 
in  length  could  scarcely  magnify  200  times.  You 
must  be  sensible,  therefore,  that  the  difficulty  of 
pointing  and  managing  such  an  unwieldy  machine, 
must  oppose  insurmountable  obstacles  to  pushing 
the  experiment  further.  The  famous  Hevelius,  the 

VOL.  II.— D  d 


314  OF    POCKET-GLASSES. 

astronomer  at  Dantzic,  employed  telescopes  200 
feet  long ;  but  such  instruments  must  undoubtedly 
have  been  very  defective,  as  the  same  things  are 
now  discovered  by  instruments  much  shorter. 

This  is  a  brief  general  description  of  telescopes, 
and  of  the  different  kinds  of  them,  which  it  is  of 
importance  carefully  to  remark,  before  we  enter  into 
a  detail  of  their  construction,  and  of  the  manner  in 
which  two  or  more  lenses  are  united,  in  order  to 
produce  all  the  different  effects. 

2d  February,  1762. 


LETTER  LXXXIX. 

Of  Pocket-glasses. 

We  have  no  certain  information  respecting  the 
person  to  whom  we  are  indebted  for  the  discovery 
of  the  telescope :  whether  he  were  a  Dutch  artist,  or 
an  Italian  of  the  name  of  Porta.*  Whoever  he  was, 
it  is  almost  one  hundred  and  fifty  years  since  small 
pocket-glasses  were  first  constructed,  composed  of 
two  lenses,  of  which  the  one  was  convex,  and  the 
other  concave.  To  pure  chance,  perhaps,  a  disco- 
very of  so  much  utility  is  to  be  ascribed.  It  was 
possible,  without  design,  to  place  two  lenses  nearer 
to  or  farther  from  each  other,  till  the  object  appeared 
distinctly. 

The  convex  lens  PAP,  Fig.  166  is  directed  towards 
Fig.  166. 


*  If  the  telescope  was  not  actually  invented  by  Roger  Bacon,  or 
Leonard  Digges,  they  at  least  constructed  combinations  of  lenses  and 
mirrors  which  produced  the  same  effect. — Ed. 


OF    POCKET-GLASSES.  315 

the  object,  and  the  eye  is  applied  to  the  concave 
lens  Q  B  Q ;  for  which  reason,  the  lens  P  A  P  is 
named  the  object-glass,  and  Q  B  Q  the  eye-glass. 
These  two  lenses  are  disposed  on  the  same  axis 
A  B,  perpendicular  to  both,  and  passing  through  their 
centres.  The  focal  distance  of  the  convex  lens 
PAP  must  be  greater  than  that  of  the  concave  ;  and 
the  lenses  must  be  disposed  in  such  a  manner,  that 
if  A  F  be  the  focal  distance  of  the  objective  PAP, 
the  focus  of  the  eye-glass  Q  Q  B  must  fall  at  the  same 
point  F;  accordingly,  the  interval  between  the  lenses 
A  and  B  is  the  difference  between  the  focal  dis- 
tances of  the  two  lenses,  A  F  being  the  focal  distance 
of  the  object-glass,  and  B  F  that  of  the  eye-glass. 
When  the  lenses  are  arranged,  a  person  with  good 
eyes  will  clearly  see  distant  objects,  which  will  ap- 
pear as  many  times  greater  as  the  line  A  F  is  greater 
than  B  F.  Thus,  supposing  the  focal  distance  of  the 
object-glass  to  be  six  inches,  and  that  of  the  eye- 
glass one  inch,  the  object  will  be  magnified  six  times, 
or  will  appear  under  an  angle  six  times  greater  than 
when  viewed  with  the  naked  eye ;  and,  in  this  case, 
the  interval  between  the  lenses  A,  B  will  be  five 
inches,  which  is,  at  the  same  time,  the  length  of  the 
instrument.  There  is  no  need  to  inform  you  that 
these  two  lenses  are  cased  in  a  tube  of  the  same 
length,  though  not  thus  represented  in  the  figure. 

Having  shown  in  what  manner  the  two  lenses  are 
to  be  joined  together,  in  order  to  produce  a  good 
instrument,  two  things  must  be  explained  to  you : 
the  one,  How  these  lenses  come  to  represent  objects 
distinctly ;  and  the  other,  Why  they  appear  magni- 
fied as  many  times  as  the  line  A  F  exceeds  the  line 
B  F.  W^ith  respect  to  the  first,  it  must  be  remarked, 
that  a  good  eye  sees  objects  best,  when  they  are  so 
distant  that  the  rays  which  fall  on  the  eye  may  be 
considered  as  parallel  to  each  other. 

Let  us  consider,  then,  a  point  V,  Fig.  167,  in  the 
object  towards  which  the  instrument  is  directed,  and 
on  the  supposition  of  its  being  very  distant,  the  rays 


316 


OF    POCKET-GLASSES. 


which  fall  on  the  object-glass  PQ,0  A,  Pig.  167. 
P  Q,  will  be  almost  parallel  to  each 
other;  accordingly,  the  object-glass, 
Q  A  Q,  being  a  convex  lens,  will  collect 
them  in  its  focus  F,  so  that  these  rays, 
being  convergent,  will  not  suit  a  good 
eye.  But  the  concave  lens  at  B,  hav- 
ing the  power  of  rendering  the  rays 
more  divergent,  or  of  diminishing  their 
convergency,  will  refract  the  rays  Q  R, 
Q  R,  so  that  they  shall  become  parallel 
to  each  other ;  that  is,  instead  of  meet- 
ing in  the  point  F,  they  will  assume  the 
direction  R  S,  R  S,  parallel  to  the  axis 
B  F.  Thus  a  good  eye,  according  to 
which  the  construction  of  these  is 
always  regulated,  on  receiving  these 
parallel  rays  R  S,  B  F,  R  S,  will  see 
the  object  distinctly.  The  rays  R  S,  R  S  become 
exactly  parallel  to  each  other,  because  the  concave 
lens  has  its  focus,  or  rather  its  point  of  dispersion,  at  F. 

You  have  only  to  recollect,  that  when  parallel 
rays  fall  on  a  concave  lens,  they  become  divergent 
by  refraction,  so  that  being  produced  backward,  they 
meet  in  the  focus.  This  being  laid  down,  we  have 
only  to  reverse  the  case,  and  to  consider  the  rays 
S  R,  S  R,  as  falling  on  the  concave  lens :  in  this  case 
it  is  certain  they  would  assume  the  directions  R  Q, 
R  Q,  which  produced  backwards  would  meet  in  the 
point  F,  which  is  the  common  focus  of  the  convex 
and  concave  lenses.  Now  it  is  a  general  law,  that  in 
whatever  manner  rays  are  refracted  in  their  passage 
from  one  place  to  another,  they  must  always  undergo 
the  same  refractions  in  returning  from  the  last  to  the 
first.  If,  therefore,  the  refracted  rays  R  Q,  R  Q 
correspond  to  the  incident  rays  S  R,  S  R ;  then,  re- 
ciprocally, the  rays  Q  R,  Q  R,  being  the  incident  ones, 
the  refracted  rays  will  be  R  S  and  R  S. 

The  matter  will  perhaps  appear  in  a  clearer  light 
still,  when  I  sav  that  concave  lenses  have  the  power 


OF   POCKET-GLASSES. 


317 


of  renderingparallel  those  rays  which,  without  the  re- 
fraction, would  proceed  to  their  focus.  You  will  please 
carefully  to  attend  to  the  following  laws  of  refraction, 
which  apply  to  both  convex  and  concave  lenses. 


Fte.  168. 


1.  By  a  convex 
lens,  Fig.  168,  paral- 
lel rays  are  rendered 
convergent. 


Fig.  169. 


Convergent  rays  become 
still  more  so,  Fig.  169,  and 
divergent  less  divergent. 


2.  By  a  concave  lens 
parallel  rays  are  rendered 
divergent.  Fig.  170. 


Divergent  rays  be- 
come still  more  diver- 
gent, Fig.  171,  and 
convergent  rays  less 
convergent. 


All  this  is  founded  on  the  nature  of  refraction  and 
the  figure  of  the  lenses,  the  discussion  of  which 
would  require  a  very  long  detail ;  but  the  two  rules 
which  1  have  now  laid  down  contain  all  that  is 
essential.  It  is  abundantly  evident,  then,  that  when 
the  convex  and  the  concave  lenses  are  so  combined 
that  they  acquire  a  common  focus  at  F,  they  will 
distinctly  represent  distant  objects,  because  the 
parallelism  of  the  rays  is  restored  by  the  concave 
lens  after  the  convex  lens  had  rendered  them  con- 
Dd2 


318 


MAGNIFYING    POWER    OF 


vergent.  In  other  words,  the  rays  of  very  distant 
objects,  being  nearly  parallel  to  each  other,  become 
convergent  by  a  convex  lens;  and  afterward,  the 
concave  lens  destroys  this  convergency,  and  again 
renders  the  rays  parallel  to  each  other. 
Qth  February,  1762. 


LETTER  XC. 

On  the  magnifying  Power  of  Pocket-glasses. 

THE  principal  article  respecting  telescopical  in- 
struments remains  still  to  be  explained,  namely,  their 
effect  in  magnifying  objects.  I  hope  to  place  this  in 
so  clear  a  light  as  to  remove  every  difficulty  in  which 
the  subject  may  be  involved;  and  for  this  purpose  I 
shall  comprise  what  I  have  to  say  in  the  following 
propositions. 

1.  Let  E   e,   Fig.  172,  be  the   object,  Fig.  172. 
situated  on  the  axis  of  the  instrument,       _       „ 
which  passes  perpendicularly  through  both 

lenses  in  their  centres.  This  object  E  e 
must  be  considered  as  at  an  infinite  dis- 
tance. 

2.  If,  then,  the  eye,  placed  at  A,  looks 
at  this   object,  it  will  appear  under  the 
angle  E  A  e,  called  its  visual  angle.     It 
will,  accordingly,  be  necessary  to  prove, 
that  on  looking  at  the  same  object  through 
the  glass  it  will  appear  under  a  greater 
angle,  and  exactly  as  many  times  greater 
as  the  focal  distance  of  the  object-glass 
PAP  exceeds  that  of  the  eye-glass 
QBQ. 

3.  As  the  effect  of  all  lenses  consists 
in   representing  the  objects   in   another 
place,  and  with  a  certain  magnitude,  we 
have  only  to  examine  the  images  which 
Siiall  be  successively  represented  by  the 


POCKET-GLASSES.  319 

two  lenses,  the  last  of  which  is  the  immediate  ob- 
ject of  the  sight  of  the  person  who  looks  through 
the  instrument. 

4.  Now,  the  object  E  e  being  infinitely  distant  from 
the  convex  lens  PAP,  its  image  will  be  represented 
behind  the  lens  at  F/,  so  that  A  F  shall  be  equal  to 
the  focal  distance  of  the  lens ;  and  the  magnitude 
of  this  image  F  /  is  determined  by  the  straight  line 
f  A  e,  drawn  from  the  extremity  of  the  object  e, 
through  the  centre  of  the  lens  A,  by  which  we  see 
that  this  image  is  inverted,  and  as  many  times 
smaller  than  the  object  as  the  distance  A  F  is  smaller 
than  the  distance  A  E. 

5.  Again,  this  image  F/  holds  the  place  of  the 
object  relatively  to  the  eye-glass  Q  B  Q,  as  the  rays 
which  fall  on  this  lens  are  precisely  those  which 
would  almost  form  the  image  F/,  but  are  intercepted 
in  their  progress  by  the  concave  lens  Q  B  Q ;  so 
that  this  image  is  only  imaginary :  the  effect,  how- 
ever, is  the  same  as  if  it  were  real. 

6.  This  image  F  /,  which  we  are  now  consider- 
ing as  an  object  being  at  the  focal  distance  of  the 
lens  Q  B  Q,  will  be  transported  almost  to  infinity 
by  the  refraction  of  this  lens.     The  preceding  figure 
marks  this  new  image  at  G  g,  whose  distance  A  G 
must  be  conceived  as  infinite,  and  the  rays,  refracted 
a  second  time  by  the  lens  Q  B  Q,  will  pursue  the 
same  direction  as  if  they  actually  proceeded  from 
the  image  G  g. 

7.  This  second  image  G  g  being,  then,  the  object 
of  the  person  who  looks  through  the  instrument,  its 
magnitude  falls  to  be  considered.     To  this  effect, 
as  it  is  produced  by  the  first  image  F/  from  the 
refraction  of  the  lens  Q  B  Q,  following  the  general 
rule,  we  have  only  to  draw  through  the  centre  of 
the  lens  B  a  straight  line,  which  shall  pass  through 
the  point  /  of  the  first  image,  and  that  line  will 
mark  at  g  the  extremity  of  the  second  image. 

8.  Let  the  spectator  now   apply  his  eye  to  B 
and  as  the  rays  which  it  receives  pursue  the  same 


320  MAGNIFYING    POWER    OF 

direction  as  if  they  actually  proceeded  from  the 
image  G  g,  it  will  appear  to  him  under  the  angle 
G  B  g,  which  is  greater  than  the  angle  E  A  e,  under 
which  the  object  E  e  appears  to  the  naked  eye. 

9.  In  order  the  better  to  compare  these  two  an- 
gles, it  is  evident,  first,  that  the  angle  E  A  e  is  equal 
to  the  angle  FA/,  being  vertical  angles;  for  the 
same  reason,  the  angle  G  B  g-  is  equal  to  the  angle 
F  B  /,  being  vertical  and  opposite  at  the  point  B. 
It  remains  to  be  proved,  therefore,  that  the  angle 
F  B  /  exceeds  the  angle  F  A  /  as  many  times  as 
the  line  A  F  exceeds  the  line  B  /;  the  former  of 
which,  A  F,  is  the  focal  distance  of  the  object-glass, 
and  the  other,  B  F,  the  focal  distance  of  the  eye- 
glass. 

10.  In  order  to  demonstrate  this,  we  must  have 
recourse  to  certain  geometrical  propositions  respect- 
ing the  nature  of  sectors.     You  will  recollect  that 
the  sector  is  part  of  a  circle  contained  between  two 
radii  C  M  and  C  N,  Fig.  173,  and       Pig.' 173. 

an  arch  or  portion  of  the  circum- 
ference  M  N.  In  a  sector,  then, 
there  are  three  things  to  be  con- 
sidered :  1.  The  radius  of  the  circle, 
C  M  or  C  N ;  2.  The  quantity  of 
the  arch  M  N ;  3.  The  angle  M  C  N. 

11.  Let  us  now  consider  two  sec- 
tors,  M  C  N  and  men,  whose  radii 
C  M  and  c  m  are  equal  to  each  other ; 
now  it  is  demonstrated  in  the  ele- 
ments of  geometry,  that  the  angles 
C  and  c  have  the  same  proportion 
to  each  other  that  the  arches  M  IV 
and  m  n  have  :  in  other  words,  the 
angle  C  is  as  many  times  greater 
than  the  angle  c,  as  the  arch  M  N  is 

greater  than  the  arch  m  n ;  but,  instead  of  this  awk- 
ward mode  of  expression,  we  say  that  the  angles  C 
and  c  are  proportional  to  the  arches  M  N  and  m  n, 
the  radii  being  equal 


POCKET-GLASSES.  321 

12.  Let  us  likewise  consider  two  sectors,  M  C  N 
and  men,  Fig.   174,   whose  p-     1?4 
angles  C  and  c  are  equal  to 

each  other,  but  the  radii  un- 
equal :  and  it  is  demonstrated 
in  geometry,  that  the  arch  M  N  %L 
is  as  many  times  greater  than  \/c 
the  arch  m  n,  as  the  radius  CM7 
is  greater  than  the  radius  c  m ; 
or,  in  geometrical  language, 
the  arches  are  in  proportion  to  the  radii,  the  angles 
being  equal.  The  reason  is  obvious,  for  every  arch 
contains  as  many  degrees  as  its  angle ;  and  the  de- 
grees of  a  great  circle  exceed  those  of  a  small  one 
as  many  times  as  the  greater  radius  exceeds  the 
smaller. 

13.  Finally,  let  us  consider  likewise    the  case 
when,  as  in  the  two  sectors  M  C  N  and  men, 
Fig.  175,  the  arches  M  N  and  m  n  are    Fig.  175. 
equal;  but  the  radii  C  M  and  c  m  un-     M 
equal. 

In  this  case,  the  angle  C,  which  cor- 
responds to  the  greater  radius  C  M,  is 
the  smaller,  and  the  angle  c,  which  cor- 
responds to  the  smaller  radius  c  m,  is 
the  greater;  and  this  in  the  same  pro- 
portion  as  the  radii.  That  is,  the  angle 
c  is  as  many  times  greater  than  the 
angle  C  as  the  radius  C  M  is  greater  than  the  radius 
cm-,  or,  to  speak  geometrically,  the  angles  are  re- 
ciprocally proportional  to  the  radii,  the  arches  being 
equal. 

14.  This  last  proposition  carries  me  forward  to 
my  conclusion,  after  I  have  subjoined  this  remark, 
that  when  the  angles  are  very  small,  as  in  the  case 
of  pocket-glasses,  there  is  no  sensible  difference  in 
the  chords  of  the  arches  M  N  and  m  n,  that  is,  of 
the  straight  lines  M  N  and  m  n. 

15.  Having  made  this  remark,  we  return  to  Fig.  172 
(p.  318).    The  triangles  F  A  /  and  F  B  /  may  be 


322  DEFECTS    OF    POCKET-GLASSES. 

considered  as  sectors,  in  which  the  arch  F/  is  the 
same  in  both.  Consequently,  the  angle  F  B  /  ex- 
ceeds the  angle  F  A  /  as  often  as  the  distance  A  F 
exceeds  the  distance  B  F.  That  is,  the  object  E  e 
will  appear  through  the  instrument  under  an  pngle 
as  many  times  greater  as  the  focal  distance  of  the 
object-glass  A  F  exceeds  the  focal  distance  of  the 
eye-glass  B  F,  which  was  the  thing  to  be  demon- 
strated. 

9th  February,  1762. 


LETTER  XCI. 

Defects  of  Pocket-glasses.     Of  the  apparent  Field. 

You  must  be  sensible  that  no  great  advantage  is 
to  be  expected  from  such  small  instruments  ;  and  it 
has  already  been  remarked  that  they  do  not  mag- 
nify objects  above  ten  times.  Were  the  effect  to  be 
carried  further,  not  only  would  the  length  .become 
too  great  to  admit  of  their  being  carried  about  in 
the  pocket,  but  they  would  become  subject  to  other 
and  more  essential  defects.  This  has  induced  art- 
ists entirely  to  lay  aside  glasses  of  this  sort,  when 
superior  effect  is  required. 

The  principal  of  these  defects  is  the  smallness 
of  the  apparent  field ;  and  this  leads  me  to  explain 
an  important  article  relative  to  telescopes  of  every 
description.  When  a  telescope  is  directed  towards 
the  heavens,  or  to  very  distant  objects  on  the  earth, 
the  space  discovered  appears  in  the  figure  of  a  cir- 
cle, and  we  see  those  objects  only  which  are  included 
in  that  space;  so  that  if  you  wished  to  examine 
other  objects,  the  position  of  the  instrument  must 
be  altered.  This  circular  space,  presented  to  the 
eye  of  the  spectator,  is  denominated  the  apparent 
field,  or,  in  one  word,  the  field  of  the  instrument ; 
and  it  is  abundantly  obvious,  that  it  must  be  a  great 


DEFECTS    OF   POCKET-GLASSES,  323 

advantage  to  have  a  very  large  field,  and  that,  on 
the  contrary,  a  small  field  is  a  very  great  inconve- 
nience in  instruments  of  this  sort.  Let  us  suppose 
two  telescopes  directed  towards  the  moon,  by  the 
one  of  which  we  can  discover  only  the  half  of  that 
luminary,  whereas  by  the  other  we  see  her  whole 
body,  together  with  the  neighbouring  stars  ;  the  field 
of  this  last  is  therefore  much  greater  than  that  of 
the  other.  That  which  presents  the  greater  field 
relieves  us,  not  only  from  the  trouble  of  frequently 
changing  the  position,  but  procures  another  very 
great  advantage ;  that  of  enabling  us  to  compare, 
by  viewing  them  at  the  same  time,  several  parts  of 
the  object  one  with  another. 

It  is  therefore  one  of  the  greatest  perfections  of 
a  telescope  to  present  a  very  ample  field ;  and  it  is 
accordingly  a  matter  of  much  importance  to  mea- 
sure the  field  of  every  instrument.  In  this  view, 
we  are  regulated  by  the  heavens,  and  we  determine 
the  circular  space  seen  through  a  telescope,  by 
measuring  its  diameter  in  degrees  and  minutes. 
Thus,  the  apparent  diameter  of  the  full  moon  being 
about  half  a  degree,  if  a  telescope  takes  in  the  moon 
only,  we  say  that  the  diameter  of  its  field  is  half  a 
degree  ;  and  if  you  could  see  at  once  only  the  half 
of  the  moon,  the  diameter  of  the  field  would  be  the 
quarter  of  a  degree. 

The  measurement  of  angles,  then,  furnishes  the 
means  of  measuring  the  apparent  field ;  besides,  the 
thing  is  sufficiently  clear  of  itself.  Supposing  we 
could  see  through  the  instrument  A  B,  Fig.  176,  only 
the  space  POP,  and 
the  objects  which  it 
contains ;  this  space 
being  a  circle,  its 
diameter  will  be  the 
line  POP,  whose  mid- 
d'.e  point  0  is  in  the 
axis  of  the  instrument. 


324  DEFECTS   OF   POCKET-GLASSES. 

Drawing,  therefore,  from  the  extremities  P  P 
the  straight  lines  P  C,  P  C,  the  angle  PGP  will 
express  the  diameter  of  the  apparent  field;  and 
the  half  of  this  angle,  O  C  P,  is  denominated  the 
semi-diameter  of  the  apparent  field  of  such  an  in- 
strument. You  will  perfectly  comprehend  the 
meaning,  then,  when  it  is  said  that  the  diameter  of 
the  apparent  field  of  such  an  instrument  is  one  de- 
gree, that  of  another  two  degrees,  and  so  on;  as 
also  when  it  is  marked  by  minutes,  as  30  minutes, 
which  make  half  a  degree,  or  15  minutes,  which 
make  the  fourth  part  of  a  degree. 

But  in  order  to  form  a  right  judgment  of  the  value 
of  a  telescope,  with  respect  to  the  apparent  field, 
we  must  likewise  attend  to  the  magnifying  power 
of  the  instrument.  It  may  be  remarked  in  general, 
that  the  more  a  telescope  magnifies,  the  smaller,  of 
necessity,  must  be  the  apparent  field ;  these  are  the 
bounds  which  nature  herself  has  prescribed.  Let 
us  suppose  an  instrument  which  should  magnify  100 
times ;  it  is  evident  that  the  diameter  of  the  field 
could  not  possibly  be  so  much  as  two  degrees ;  for, 
as  this  space  would  appear  100  times  greater,  it 
would  resemble  a  space  of  two  hundred  degrees ; 
greater,  of  consequence,  than  the  whole  visible 
heavens,  which,  from  the  one  extremity  to  the  other, 
contain  only  180  degrees,  and  of  which  we  can  see 
but  the  half  at  most  at  once, — that  is,  a  circular  space 
of  90  degrees  in  diameter.  From  this  you  see,  that 
a  telescope  which  magnifies  100  times  could  not 
contain  a  field  of  so  much  as  one  degree  ;  for  this 
degree  multiplied  100  times  would  give  more  than 
90  degrees  ;  and  that,  accordingly,  a  telescope  which 
magnified  100  times  would  be  excellent,  if  the  diame- 
ter of  its  field  were  somewhat  less  than  one  degree  ; 
and  the  very  nature  of  the  instrument  admits  not 
of  a  greater  effect. 

But  another  telescope  which  should  magnify  only 
10  times  would  be  extremely  defective,  if  it  di»- 


DEFECTS    OF    POCKET-GLASSES.  325 

covered  a  field  of  only  one  degree  in  diameter ;  as 
this  field  magnified  10  times  would  give  a  space  of 
no  more  than  10  degrees  in  the  heavens,  which 
would  be  a  small  matter,  by  setting  too  narrow 
bounds  to  our  view.  We  should  have  good  reason, 
then,  to  reject  such  an  instrument  altogether.  Thus 
it  would  be  very  easy,  with  respect  to  the  apparent 
field,  to  form  a  judgment  of  the  excellence  or  de- 
fectiveness  of  instruments  of  this  sort,  when  the 
effect  is  taken  into  consideration.  For  when  it 
magnifies  only  10  times,  it  may  fairly  be  conjectured 
that  it  discovers  a  field  of  9  degrees  ;  as  9  degrees 
taken  10  times  give  90  degrees,  a  space  which  our 
sight  is  capable  of  embracing :  and  if  the  diameter 
of  its  field  were  only  5  degrees  or  less,  this  would 
be  an  instrument  very  defective  indeed.  Now,  I 
shall  be  able  to  demonstrate,  that  if  a  telescope 
were  to  be  constructed  such  as  I  have  been  de- 
scribing, which  should  magnify  more  than  10  times, 
it  would  be  liable  to  this  defect :  the  apparent  field 
multiplied  by  the  magnifying  power  would  be  very 
considerably  under  90  degrees,  and  would  not  even 
show  the  half.  But  when  a  small  effect  is  aimed 
at,  this  defect  is  not  so  sensible ;  for  if  such  an  in- 
strument magnifies  only  5  times,  the  diameter  of  its 
field  is  about  4  degrees,  which  magnified  5  times 
contains  a  space  of  20  degrees,  with  which  we  have 
reason  to  be  satisfied  :  but  if  we  wished  to  magnify 
25  times,  the  diameter  of  the  field  would  be  only 
half  a  degree,  which  taken  25  times  would  give 
little  more  than  12  degrees,  which  is  too  little. 
When,  therefore,  we  would  magnify  very  much,  a 
different  arrangement  of  lenses  must  be  employed, 
which  I  shall  afterward  explain. 
13th  February,  1762. 


VOL.  II.— E  e 


326  DETERMINATION  OF  THE  APPARENT 


LETTER  XCII. 

Determination  of  the  apparent  Field  for  Pocket- 
Glasses. 

To  ascertain  the  apparent  field  being  of  very 
great  importance  in  the  construction  of  telescopes, 
I  proceed  to  the  application  of  it  to  the  small 
glasses  which  I  have  been  describing. 

The  lens  PAP,  Fig.  172  (p.  318),  is  the  object-glass, 
Q  B  Q  the  eye-glass,  and  the  straight  line  E  F  the  axis 
of  the  instrument,  in  which  is  seen,  at  a  very  great 
distance,  through  the  instrument,  the  object  E  e, 
under  the  angle  E  A  e,  which  represents  the  semi- 
diameter  of  the  apparent  field,  for  it  extends  as 
far  on  the  other  side  downwards.  The  point  E, 
then,  is  the  centre  of  the  space  seen  through  the 
instrument,  the  radius  of  which,  E  A,  as  it  passes 
perpendicularly  through  both  lenses,  undergoes  no 
refraction;  and  in  order  that  this  ray  may  have 
admission  into  the  eye,  the  eye  must  be  fixed  some- 
where on  the  axis  of  the  instrument  B  F,  behind 
the  eye-glass,  so  that  the  centre  of  the  pupil  shall 
be  in  the  line  B  F ;  and  this  is  a  general  rule  for 
every  species  of  telescope.  Let  us  now  consider 
the  visible  extremity  of  the  object  e,  whose  rays 
exactly  fill  the  whole  opening  of  the  object-glass 
PAP;  but  it  will  be  sufficient  to  attend  only  to  the 
ray  E  A,  which  passes  through  the  centre  of  the 
object-glass  A,  as  the  others  surround,  and  little 
more  than  strengthen  this  ray :  so  that  if  it  is  ad- 
mitted into  the  eye,  the  others,  or  at  least  a  con- 
siderable part  of  them,  find  admission  likewise  ;  and 
if  this  ray  is  not  admitted  into  the  eye,  though  per- 
haps some  of  the  others  may  enter,  they  are  too 
feeble  to  excite  an  impression  sufficiently  powerful. 


FIELD    FOR   POCKET-GLASSES.  327 

Hence  this  may  be  laid  down  as  a  rule,  that  the  ex- 
tremity e  of  the  object  is  seen  only  so  far  as  the  ray 
e  A,  after  having  passed  through  the  two  lenses,  is 
admitted  into  the  eye. 

We  must  therefore  carefully  examine  the  direc- 
tion of  this  ray  e  A.  Now,  as  it  passes  through  the 
centre  of  the  object-glass  A,  it  undergoes  no  refrac- 
tion ;  conformably  to  the  rule  laid  down  from  the 
beginning,  that  rays  passing  through  the  centre  of 
any  lens  whatever  are  not  diverted  from  their  direc- 
tion, that  is,  undergo  no  refraction.  This  ray,  e  A, 
therefore,  after  having  passed  through  the  object- 
glass,  would  continue  in  the  same  direction,  to  meet 
the  other  rays  issuing  from  the  same  point  e,  to  the 
point/ of  the  image  represented  by  the  object-glass 
at  F/,  the  point  /  being  the  image  of  the  point  e 
of  the  object ;  but  the  ray  meeting  at  m,  the  concave 
lens,  but  not  in  its  centre,  will  be  diverted  from  that 
direction  ;  and  instead  of  terminating  in  /,  will  as- 
sume the  direction  m  n,  more  divergent  from  B  F,  it 
being  the  natural  effect  of  concave  lenses  to  render 
rays  always  more  divergent.  In  order  to  ascertain 
this  new  direction  m  n,  you  will  please  to  recollect 
that,  the  object-glass  represents  the  object  E  e  in  an 
inverted  position  at  F/,  so  that  A  F  is  equal  to  the 
focal  distance  of  this  lens,  which  transports  the  ob- 
ject E  e  to  F/.  Then  this  image  F/  occupies  the 
place  of  the  object  with  respect  to  the  eye-glass 
Q  B  Q,  which,  in  its  turn,  transports  that  image  to 
G  g,  whose  distance  B  G  must  be  as  great  as  that 
of  the  object  itself:  and  for  this  effect,  it  is  neces- 
sary to  place  the  eye-glass  in  such  a  manner  that 
the  interval  B  F  shall  be  equal  to  its  focal  distance. 

As  to  the  magnitude  of  these  images,  the  first  F/ 
is  determined  by  the  straight  line  e  A/,  drawn  from 
e  through  the  centre  A  of  the  first  lens ;  and  the 
other  G  g  by  the  straight  line/B  «•,  drawn  from  the 
point  /  through  the  centre  B  of  the  second  lens. 


328       APPARENT  FIELD  FOR  POCKET-GLASSES. 

This  being  laid  down,  the  ray  A  m  directed  towards 
the  point  f  is  refracted,  and  proceeds  in  the  direc- 
tion m  n ;  and  this  line  m  n,  being  produced  back- 
wards, will  pass  through  the  point  g,  for  m  n  has  the 
same  effect  in  the  eye  as  if  it  actually  proceeded 
from  the  point  g.  Now,  as  this  line  m  n  retires  far- 
ther and  farther  from  the  axis  B  F,  where  the  centre 
of  the  pupil  is,  it  cannot  enter  into  the  eye,  unless 
the  opening  of  the  pupil  extends  so  far ;  and  if  the 
opening  of  the  pupil  were  reduced  to  nothing, 
the  ray  m  n  would  be  excluded  from  the  eye,  and 
the  point  e  of  the  object  could  not  be  visible,  nor 
even  any  other  point  of  the  object  out  of  the  axis 
A  F.  There  would,  therefore,  be  no  apparent  field, 
and  nothing  would  be  seen  through  such  an  instru- 
ment except  the  single  point  E  of  the  object,  which 
is  in  its  axis.  It  is  evident,  then,  that  a  telescope 
of  this  sort  discovers  no  field  but  as  far  as  the  pupil 
expands ;  so  that  in  proportion  as  the  expansion  of 
the  pupil  is  greater  or  less,  so  likewise  the  appa- 
rent field  is  great  or  small.  In  this  case  the  point  e 
will  therefore  be  still  visible  to  the  eye  if  the  small 
interval  B  m  does  not  exceed  half  the  diameter  of 
the  eye,  that  the  ray  m  n  may  find  admission  into  it ; 
but  in  this  case,  likewise,  the  eye  must  be  brought 
as  close  as  possible  to  the  eye-glass  :  for  as  the  ray 
m  n  removes  from  the  axis  F  B,  it  would  escape  the 
pupil  at  a  greater  distance. 

Now  it  is  easy  to  determine  the  apparent  field 
which  such  an  instrument  would  discover  on  the 
eye-glass  :  you  have  only  to  take  the  interval  B  m 
equal  to  the  semi-diameter  of  the  pupil,  and  to  draw 
through  that  point  m,  and  the  centre  of  the  object- 
glass  A,  the  straight  line  m  A  e ;  then  this  line  will 
mark  on  the  object  the  extremity  e,  which  will  be 
still  visible  through  the  instrument,  and  the  angle 
E  A  e  will  give  the  semi-diameter  of  the  apparent 
field.  Hence  you  will  easily  judge,  that  whenever 


ASTRONOMICAL   TELESCOPES.  329 

the  distance  of  the  lenses  A  B  exceeds  some  inches, 
the  angle  B  A  m  must  become  extremely  small,  as 
the  line  or  the  distance  B  m  is  but  about  the  twen- 
tieth part  of  an  inch.  Now  if  it  were  intended  to 
magnify  very  much,  the  distance  of  the  lenses  must 
become  considerable,  and  the  consequence  would 
be  that  the  apparent  field  must  become  extremely 
small.  The  structure  of  the  human  eye,  then,  sets 
bounds  to  telescopes  of  this  description,  and  obliges 
us  to  have  recourse  to  others  of  a  different  construc- 
tion whenever  we  want  to  produce  very  considerable 
effects. 

L6th  February,  1762. 


LETTER  XCIII. 

Astronomical  Telescopes,  and  their  magnifying  Power. 

I  PROCEED  to  the  second  species  of  telescopes, 
called  astronomical,  and  remark,  that  they  consist 
of  only  two  lenses,  like  those  of  the  first  species  ; 
with  this  difference,  that  in  the  construction  of  astro- 
nomical telescopes,  instead  of  a  concave  eye-glass, 
we  employ  a  convex  one. 

The  object-glass  PAP,  Fig.  177,  is,  as  in  the  other 

Fig.  177. 


species,  convex,  whose  focus  being  at  F,  we  place, 
on  the  same  axis  a  smaller  convex  lens  Q  Q,  in  such 
a  manner  that  its  focus  shall  likewise  fall  on  the 
same  point  F.  Then  placing  the  eye  at  0,  so  that 
the  distance  B  0  shall  be  nearly  equal  to  the  focal 
Ee  2 


330     ASTRONOMICAL  TELESCOPES,  AND 

distance  of  the  eye-glass  Q  Q,  you  will  see  objects 
distinctly,  and  magnified  as  many  times  as  the  focal 
distance  of  the  object-glass  A  F  shall  exceed  that  of 
the  eye-glass  B  F :  but  it  is  to  be  remarked  that 
every  object  will  appear  in  an  inverted  position ;  so 
that  if  the  instrument  were  to  be  pointed  towards  a 
house,  the  roof  would  appear  undermost,  and  the 
ground-floor  uppermost.  As  this  circumstance 
would  be  awkward  in  viewing  terrestrial  objects, 
which  we  never  see  in  an  inverted  situation,  the 
use  of  this  species  of  telescopes  is  confined  to  the 
heavenly  bodies,  it  being  a  matter  of  indifference  in 
what  direction  they  appear ;  it  is  sufficient  to  the 
astronomer  to  know  that  what  he  sees  uppermost  is 
really  undermost,  and  reciprocally.  Nothing,  how- 
ever, forbids  the  application  of  such  telescopes  to  ter- 
restrial objects  ;  the  eye  soon  becomes  accustomed 
to  the  inverted  position,  provided  the  object  is  seen 
distinctly,  and  very  much  magnified. 

Having  given  this  description,  three  things  fall  to 
be  demonstrated :  first,  that  by  this  arrangement  of 
'the  lenses  objects  must  appear  distinctly ;  secondly, 
that  they  must  appear  magnified  as  many  times  as 
the  focal  distance  of  the  object-glass  exceeds  that 
of  the  eye-glass,  and  in  an  inverted  position ;  and 
thirdly,  that  the  eye  must  not  be  applied  close  to  the 
eye-glass,  as  in  the  first  species,  but  must  be  removed 
to  nearly  the  focal  distance  of  the  ocular. 

1.  As  to  the  first,  it  is  demonstrated  in  the  same 
manner  as  in  the  preceding  case  :  the  rays  e  P,  e  P, 
which  are  parallel  before  they  enter  into  the  object- 
glass,  meet  by  refraction  in  the  focus  of  this  lens  at 
F  ;  the  eye-glass  must,  of  course,  restore  the  paral- 
lelism of  these  rays,  and  distinct  vision  requires 
that  the  rays  proceeding  from  every  point  should 
be  nearly  parallel  to  each  other  when  they  enter  the 
eye.  Now,  the  eye-glass,  having  its  focus  at  F,  is 
placed  in  such  a  manner  as  to  render  the  rays  F  M, 
F  M,  by  the  refraction,  parallel,  and  consequently 


THEIR   MAGNIFYING    POWER. 


331 


178. 


the  eye  will  receive  the  rays  N  o,  N  o,  parallel  to 
each  other. 

2.  With  respect  to  the  second  article,  let  us  consider 
the  object  at  E  e,  Fig.  178,  but  so  that 
the  distance  E  A  shall  be  almost  in- 
finite. The  image  of  this  object, 
represented  by  the  object-glass,  will 
therefore  be  F/,  situated  at  the  fo- 
cal distance  of  that  lens  A  F,  and 
determined  by  the  straight  line  e  A/, 
drawn  through  the  centre  of  the 
lens.  This  image  F/,  which  is  in- 
verted, occupies  the  place  of  the 
object  with  respect  to  the  eye-glass, 
and  being  in  its  focus,  the  second 
image  will  be  again  removed  to  an 
infinite  distance  by  the  refraction 
of  this  lens,  and  will  fall,  for  exam- 
ple, at  G  g,  the  distance  A  G  being 
considered  as  infinite,  like  that  of 
A  E.  Now,  in  order  to  determine  the  magnitude  of 
this  image,  you  have  only  to  draw  through  the  centre 
B  of  the  lens,  and  the  extremity /of  the  first  image, 
the  straight  line  B/g-.  Now  this  second  image  Gg 
being  the  immediate  object  of  vision  to  the  person 
who  looks  through  the  telescope,  it  is  evident  at 
once  that  this  representation  is  inverted,  and,  as  it 
is  infinitely  distant,  will  appear  under  an  angle 
G  B  g.  But  the  object  itself  E  e  will  appear  to  the 
naked  eye  under  the  angle  E  A  e :  now  you  are  sen- 
sible, without  being  reminded,  that  it  is  indifferent 
to  take  the  points  A  and  B,  in  order -to  have  the 
visual  angles  E  A  e  and  G  B  g,  on  account  of  the 
infinite  distance  of  the  object.  You  now  see  here, 
as  in  the  preceding  case,  that  the  triangles  FA/ and 
F  B/may  be  considered  as  circular  sectors,  the  line 
F/  measuring  the  arch  of  both ;  and  the  angles  them- 
selves being  so  very  small,  no  sensible  mistake  can 
be  committed  in  taking  the  chord  for  the  arch.  As, 


332  OF   THE   APPARENT   FIELD,   AND 

then,  the  radii  of  these  two  sectors  are  the  lines  A  E 
and  B  F,  the  arches  being  equal  to  each  other,  it 
follows,  as  was  formerly  demonstrated,  that  the 
angles  FA/  (or,  which  is  the  same  thing,  E  A  e) 
and  F  B/(or,  which  is  the  same  thing,  G  B  g)  have 
the  same  proportion  to  each  other  that  the  radii 
B  F  and  A  F  have.  Therefore,  the  angle  G  B  g, 
under  which  the  object  is  seen  through  the  telescope, 
as  many  times  exceeds  the  angle  E  A  e,  under  which 
the  object  is  seen  by  the  naked  eye,  as  the  line  A  F 
exceeds  the  line  B  F ;  which  was  the  second  point 
to  be  demonstrated.  I  am  under  the  necessity  of 
deferring  the  demonstration  of  my  third  proposition 
till  next  post. 

February,  1762. 


LETTER  XCIV. 

Of  the  apparent  Field,  and  the  Place  of  the  Eye. 

IN  fulfilling  my  engagement  respecting  the  third 
particular  proposed,  namely,  to  determine  the  place 
of  the  eye  behind  the  telescope,  I  remark  that  this 
subject  is  most  intimately  connected  with  the  appa- 
rent field,  and  that  it  is  precisely  the  field  which 
obliges  us  to  keep  the  eye  fixed  at  the  proper  dis- 
tance ;  for  if  it  were  to  be  brought  closer,  or  removed 
farther  off,  we  should  no  longer  discover  so  large  a 
field. 

The  extent  of  the  field  being  an  article  of  such 
importance,  indeed  so  essential,  in  all  telescopes,  it 
must  be  of  equal  importance  to  determine  exactly 
the  place  of  the  eye  from  which  the  largest  field  is 
discoverable.  If  the  eye  were  to  be  applied  close  to 
the  eye-glass,  we  should  have  nearly  the  same  field 
as  we  have  with  the  pocket-glass,  which  becomes 
insufferably  small  whenever  the  magnifying  power 
is  considerable.  It  is  therefore  a  vast  advantage  to 


THE    PLACE    OF   THE    EYE.  333 

astronomical  telescopes,  that  by  withdrawing  the 
eye  from  the  eye-glass  the  apparent  field  increases 
to  a  certain  extent ;  and  it  is  precisely  this  which 
renders  such  telescopes  susceptible  of  prodigious 
magnifying  powers,  whereas  those  of  the  first  species 
are  in  this  respect  extremely  limited.  You  know 
that  with  the  astronomical  telescope,  the  magnifying 
power  has  been  carried  beyond  two  hundred  times, 
which  gives  them  an  inconceivable  superiority  over 
those  of  the  first  species,  which  can  scarcely  magnify 
ten  times  ;  and  the  trifling  inconvenience  of  the  in- 
verted position  is  infinitely  overbalanced  by  an  ad- 
vantage so  very  great. 

I  will  endeavour  to  put  this  important  article  in 
the  clearest  light  possible. 

1.  The  object  E  e,  Fig.  179,  being  in- 
finitely distant,  let  e  be  its  extremity, 
still  visible  through  the  telescope,  whose 
lenses  are  PAP  and  Q  B  Q,  fitted  on 
the  common  axis  E  A  B  0  ;  it  falls  to 
be  attentively  considered  what  direc- 
tion will  be  pursued  by  the  single  ray 
which   passes   from    the    extremity  e 
of  the  object,  through  the  centre  A 
of  the  object-glass.     You  will  recollect 
that  the  other  rays,  which  fall  from  the 
point  e  on  the  object-glass,  only  accom- 
pany and  strengthen  the  ray  in  question 
e  A,  which  is  the  principal  with  respect 
to  vision. 

2.  Now  this  ray  e  A,  passing  through  the  centre 
of  the  lens  P  P,  will  undergo  no  refraction,  but  will 
pursue  its  direction  in  the  straight  line  A  /m,  and 
passing  through  the   extremity  of  the  image  F  /, 
will  fall  on  the  eye-glass  at  the  point  m ;  and  here 
it  is  to  be  observed,  that  if  the  size  of  the  eye-glass 
had  not  extended  so  far  as  the  point  m,  this  ray 
would  never  have  reached  the  eye,  and  the  point  e 
would  have  been  invisible.    That  is  to  say,  it  would 


334  OF   THE  APPARENT   FIELD,   AND 

be  necessary  to  take  the  extremity  e  nearer  to  the 
axis,  in  order  that  the  ray  A/m  may  meet  the  eye- 
glass. 

3.  Now  this  ray  A  m  will  be  refracted  by  the  eye- 
glass in  a  way  which  it  is  very  easy  to  discover. 
We  have  only  to  consider  the  second  image  G  g ; 
though  infinitely  distant,  it  is  sufficient  to  know  that 
the  straight  line  B/ produced  will  pass  through  the 
extremity  g  of  the  second  image  G  g,  which  is  the 
immediate  object  of  vision.     Having  remarked  this, 
the  refracted  ray  must  assume  the  direction  n  O,  and 
this  produced  passes  through  g. 

4.  As,  therefore,  the  two  lines  0  n  and  B/meet 
at  an  infinite  distance  at  g,  they  may  be  considered 
as  parallel  to  each  other ;  and  hence  we  acquire  an 
easier  method  to  determine  the  position  of  the  re- 
fracted ray  n  O  :  you  have  only  to  draw  it  parallel 
to  the  line  B/. 

5.  Hence  it  is  clearly  evident  that  the  ray  n  0  will 
somewhere  meet  the  axis  of  the  telescope  at  O,  and 
as  usually,  when  the  magnifying  power  is  great,  the 
point  F  is  much  nearer  to  the  lens  Q  Q  than  to  the 
lens  P  P,  the  distance  B  m  will  be  somewhat  greater 
than  the  image  F/;  and  as  the  line  n  0  is  parallel 
to/B,  the  line  B  O  will  be  nearly  equal  to  B  F,  that 
is,  to  the  focal  distance  of  the  eye-glass. 

6.  If,  then,  the  eye  is  placed  at  O,  it  will  receive, 
not  only  the  rays  which  proceed  from  the  middle  of 
the  object  E,  but  those  likewise  which  proceed  from 
the  extremity  e,  and  consequently  those  also  which 
proceed  from  every  point  of  the  object;   the  eye 
would  even  receive  at  once  the  rays  B  0  and  n  O, 
even  supposing  the  pupil  infinitely  contracted.    In 
this  case,  therefore,  the  apparent  field  does  not  de- 
pend on  the  largeness  of  the  aperture  of  the  pupil, 
provided  the  eye  be  placed  at  0  ;  but  the  moment  it 
recedes^  from  this  point,  it  must  lose  considerably  in 
the  apparent  field. 

7.  If  the  point  m  were  not  in  the  extremity  of  the 


THE    PLACE    OF    THE    EYE.  335 

eye-glass,  it  would  transmit  rays  still  more  remote 
from  the  axis,  and  the  telescope  would,  of  course, 
discover  a  larger  field.  In  order,  then,  to  determine 
the  real  apparent  field  which  the  telescope  is  capable 
of  discovering,  let  there  be  drawn,  from  the  centre 
A  of  the  object-glass,  to  the  extremity  m  of  the 
eye-glass,  the  straight  line  A  m,  which,  produced  to 
the  object,  will  mark  at  e  the  visible  extremity ;  and 
consequently  the  angle  E  A  e,  or,  which  is  the  same 
thing,  the  angle  B  A  m,  will  give  the  semi-diameter 
of  the  apparent  field,  which  is  consequently  greater 
in  proportion  as  the  extent  of  the  eye-glass  is 
greater. 

8.  As,  then,  in  the  first  species  of  telescopes,  the 
apparent  field  depended  entirely  on  the  aperture  of 
the  pupil,  and  as  in  this  case  it  depends  entirely  on 
the  aperture  of  the  eye-glass,  there  is  an  essential 
difference  between  these  two  species  of  instruments, 
greatly  in  favour  of  the  latter.  The  figure  which  I 
have  employed  in  demonstrating  this  last  article  re- 
specting the  place  of  the  eye  and  the  apparent  field, 
may  greatly  assist  us  in  the  elucidation  of  the  pre- 
ceding articles. 

If  you  will  be  so  good  as  to  reflect,  that  the  object- 
glass  transports  the  object  E  e  to  F/,  and  that  the 
eye-glass  transports  it  from  F/  to  Gg-,  this  image 
Gg,  being  very  distant  from  the  immediate  object  of 
vision,  ought  to  be  seen  distinctly,  as  a  good  eye  re- 
quires a  great  distance  in  order  to  see  thus.  This 
was  the  first  article. 

As  to  the  second,  it  is  evident  at  first  sight,  that 
as  instead  of  the  real  image  E  e,  we  see  through  the 
telescope  the  image  Gg,  it  must  be  inverted.  Finally, 
this  image  is  seen  by  the  eye  placed  at  0  under  the 
angle  G  O  g,  or  B  0  n,  whereas  the  object  itself  E  e 
appears  to  the  naked  eye  under  the  angle  E  A  e  :  the 
telescope,  therefore,  magnifies  as  many  times  as  the 
angle  B  0  n  is  greater  than  the  angle  E  A  e.  Now, 
as  the  line  n  0  is  partllel  to  B/,  the  angle  B  0  n  is 


336  MAGNIFYING    POWER    OF 

equal  to  the  angle  F  B  /  and  the  angle  E  A  e  is  equal 
to  its  opposite  and  vertical  angle  FA/;  hence  the 
magnifying  power  must  be  estimated  from  the  pro- 
portion between  the  angles  F  B/  and  FA/;  accord- 
ingly, as  the  angle  F  B/ contains  the  angle  F  A/as 
often  as  the  line  A  F,  that  is,  the  focal  distance  of  the 
object-glass,  contains  the  line  B  F,  that  is,  the  focal 
distance  of  the  eye-glass,  the  magnifying  power  will 
be  therefore  expressed  by  the  proportion  of  these 
two  distances.  This  is  proof  sufficient  that  the  ele- 
ments of  geometry  may  be  successfully  employed 
in  researches  of  quite  a  different  nature — a  reflection 
not  unpleasing  to  the  mathematician. 
23d  February,  1762. 


LETTER  XCV. 

Determination  of  the  magnifying  Power  of  Astronomi- 
cal Telescopes,  and  the  Construction  of  a  Telescope 
which  shall  magnify  Objects  a  given  Number  of  Times. 

You  now  have  it  clearly  ascertained,  not  only  how 
many  times  a  proposed  instrument  will  magnify, 
but  what  is  the  mode  of  constructing  a  telescope 
which  shall  magnify  as  many  times  as  may  be 
wished.  In  the  first  case,  you  have  only  to  measure 
the  focal  distance  of  both  lenses,  the  object-glass  as 
well  as  the  eye-glass,  in  order  to  discover  how  much 
the  one  exceeds  the  other.  This  is  performed  by 
division,  and  the  quotient  indicates  the  magnifying 
power. 

Having,  then,  a  telescope,  the  focal  distance  of 
whose  object-glass  is  two  feet,  and  that  of  the  eye- 
glass one  inch,  it  is  only  necessary  to  inquire  how 
often  one  inch  is  contained  in  two  feet.  Every  one 
knows  that  a  foot  contains  twelve  inches ;  two  feet 
accordingly  contain  twenty-four  irtches,  which  are  to 
be  divided  bv  one.  But  whatever  number  we  divide 


ASTRONOMICAL    TELESCOPES.  337 

by  one  the  quotient  is  always  equal  to  the  dividend : 
if,  then,  it  is  asked,  how  often  one  inch  is  contained 
in  twenty-four  inches,  the  answer,  without  hesitation, 
is,  twenty-four  times;  consequently,  such  a  tele- 
scope magnifies  twenty-four  times,  that  is,  represents 
distant  objects  in  the  same  manner  as  if  they  were 
twenty-four  times  greater  than  they  really  are ;  in 
other  words,  you  would  see  them  through  such  a 
telescope  under  an  angle  twenty-four  times  greater 
than  by  the  naked  eye. 

Let  us  suppose  another  astronomical  telescope, 
the  focal  distance  of  whose  object-glass  is  thirty-two 
feet,  and  that  of  the  eye-glass  three  inches.  You 
see  at  once  that  these  two  lenses  must  be  placed  at 
the  distance  of  thirty-two  feet  and  three  inches  from 
each  other ;  for,  in  all  astronomical  telescopes,  the 
distance  of  the  lenses  must  be  equal  to  the  sum  of 
the  two  focal  distances,  as  has  been  already  demon- 
strated. 

To  find,  then,  how  many  times  a  telescope  of  the 
above  description  magnifies,  we  must  divide  thirty- 
two  fefcf  by  three  inches ;  and,  in  order  to  this,  re- 
duce these  thirty-two  feet  into  inches,  by  multiplying 
them  by  twelve : 

32    this  produces  384  inches ;  and  these  again 

12    divided  by  three,  the  focal  distance,  in  inches, 

3)384    of  the  eye-glass,  gives  a  quotient  of  128, 

T^g    which  indicates  that  the  proposed  telescope 
magnifies  128  times,  which  must  be  allowed 
to  be  very  considerable. 

Reciprocally,  therefore,  in  order  to  construct  a 
telescope  which  shall  magnify  a  given  number  of 
times,  say  100,  we  must  employ  two  convex  lenses, 
the  focal  distance  of  the  one  of  which  shall  be  100 
times  greater  than  that  of  the  other ;  in  this  case  the 
one  will  give  the  object-glass,  and  the  other  the  eye- 
glass. These  must  afterward  be  fitted  on  the  same 
axis,  so  that  their  distance  shall  be  equal  to  the  sum 
of  the  two  focal  distances ;  that  is,  they  must  be  fixed 

VOL.  II.— F  f 


838       POWER    OF   ASTRONOMICAL    TELESCOPES. 

in  a  tube  of  this  length,  and  then  the  eye  being  placed 
behind  the  eye-glass,  at  its  focal  distance,  will  see 
objects  magnified  100  times. 

This  arrangement  may  be  varied  without  end,  by 
assuming  an  eye-glass  at  pleasure,  and  adapting  to 
it  an  object-glass  whose  focal  distance  shall  be  100 
times  greater.  Thus,  taking  an  eye-glass  of  one 
inch  focus,  the  object-glass  must  be  of  100  inches 
focus,  and  the  distance  of  the  lenses  101  inches.  Or, 
taking  an  eye-glass  of  2  inches  focus,  the  object- 
glass  must  have  its  focus  at  the  distance  of  200 
inches,  and  the  distance  of  the  lenses  will  be  202 
inches.  If  you  were  to  take  an  eye-glass  of  3  inches 
focus,  the  focal  distance  of  the  object-glass  must  be 
300  inches,  and  the  distance  of  the  lenses  from  each 
other  303  inches.  And  if  you  were  to  take  an  eye- 
glass of  4  inches  focus,  the  object-glass  must  have 
a  focal  distance  of  400  inches,  and  the  distance  of 
the  two  lenses  404  inches,  and  so  on,  the  instrument 
always  increasing  in  length.  If,  on  the  contrary, 
you  were  to  assume  an  eye-glass  of  only  half  an 
inch  focus,  the  object-glass  must  have  a  focal  dis- 
tance of  100  half-inches,  that  is,  of  50  inches,  and 
the  distance  between  the  lenses  would  only  be  50 
inches  and  a  half,  which  is  little  more  than  four  feet. 
And  if  an  eye-glass  of  a  quarter  of  an  inch  focus 
were  to  be  employed,  the  object-glass  would  require 
a  focal  distance  of  only  100  quarters  of  an  inch,  or 
25  inches,  and  the  distance  between  the  two  lenses 
25  inches  and  a  quarter,  that  is  little  more  than  two 
feet. 

Here,  then,  are  several  methods  of  producing  the 
same  effect,  that  of  magnifying  100  times ;  and  if 
every  thing  else  were  equal,  we  should  not  hesitate 
about  giving  the  preference  to  the  last,  as  being  the 
shortest :  for  here  the  telescope,  being  reduced  to 
little  more  than  two  feet,  would  be  more  manageable 
than  one  much  longer. 

No  one,  then,  would  hesitate  about  preferring  the 


DEGREE    OF    CLEARNESS.  339 

shortest  telescopes,  provided  all  other  circumstances 
were  the  same,  and  all  the  different  species  repre- 
sented objects  in  the  same  degree  of  perfection.  But 
though  they  all  possess  the  same  magnifying  power, 
the  representation  is  by  no  means  equally  clear  and 
distinct.  That  of  two  feet  in  length  certainly  mag- 
nifies 100  times,  as  well  as  the  others ;  but  on  look- 
ing through  such  a  telescope,  objects  will  appear  not 
only  dark,  but  blunt  and  confused,  which  is  un- 
doubtedly a  very  great  defect.  The  last  telescope 
but  one,  whose  object-glass  is  50  inches  focus,  is  less 
subject  to  these  defects :  but  the  dimness  and  con- 
fusion are  still  insupportable ;  and  these  defects 
diminish  in  proportion  as  we  employ  greater  object- 
glasses,  and  are  reduced  to  almost  nothing  on  em- 
ploying an  object-glass  of  300  inches,  with  an  eye- 
glass of  3  inches  focus.  On  increasing  these  mea- 
surements, the  representation  becomes  still  clearer 
and  more  distinct ;  so  that  in  this  respect  long  tele- 
scopes are  preferable  to  short,  though  otherwise  less 
commodious.  This  circumstance  imposes  on  me  a 
new  task,  that  of  further  explaining  two  very  essen- 
tial articles  in  the  theory  of  telescopes :  the  one  re- 
spects the  clearness,  or  degree  of  light  in  which  ob- 
jects are  seen ;  and  the  other  the  distinctness  and 
accuracy  of  expression  with  which  they  are  repre- 
sented. Without  these  two  qualities,  all  magnifying 
power,  however  great,  procures  no  advantage  for  the 
contemplation  of  objects. 
27th  February,  1762. 


LETTER  XCVI. 

Degree  of  Clearness. 

IN  order  to  form  a  judgment  of  the  degree  of  clear- 
ness in  which  objects  are  represented  by  the  tele- 
scope, I  shall  recur  to  the  same  principles  which  I  en- 


340  DEGREE    OF    CLEARNESS. 

deavoured  to  elucidate  in  treating  the  same  subject 
with  reference  to  the  microscope. 

And,  first,  it  must  be  considered,  that  in  this  re- 
search it  is  not  proposed  to  determine  the  degree 
of  light  resident  in  objects  themselves,  and  which 
may  be  very  different,  not  only  in  different  bodies, 
as  being  in  their  nature  more  or  less  luminous,  but 
in  the  same  body,  according  as  circumstances  vary. 
The  same  bodies,  when  illuminated  by  the  sun,  have 
undoubtedly  more  light  than  when  the  sky  is  over- 
cast, and  in  the  night  their  light  is  wholly  extin- 
guished ;  but  different  bodies  illuminated  may  differ 
greatly  in  point  of  brightness,  according  as  their 
colours  are  more  or  less  lively.  We  are  not  inquir- 
ing, then,  into  that  light  or  brightness  which  resides 
in  objects  themselves ;  but,  be  it  strong  or  faint,  we 
say  that  a  telescope  represents  the  object  in  perfect 
clearness,  when  it  is  seen  through  the  instrument  as 
clearly  as  by  the  naked  eye ;  so  that  if  the  object  be 
dim,  we  are  not  to  expect  that  the  telescope  should 
represent  it  as  clear. 

Accordingly,  in  respect  of  clearness,  a  telescope 
is  perfect  when  it  represents  the  object  as  clearly 
as  it  appears  to  the  naked  eye.  This  takes  place,  as 
in  the  microscope,  when  the  whole  opening  of  the 
pupil  is  filled  with  the  rays  which  proceed  from 
every  point,  of  the  object,  after  being  transmitted 
through  the  telescope.  If  a  telescope  furnishes 
rays  sufficient  to  fill  the  whole  opening  of  the  pupil, 
no  greater  degree  of  clearness  need  be  desired ;  and 
supposing  it  could  supply  rays  in  greater  profusion, 
this  would  be  entirely  useless,  as  the  same  quantity 
precisely,  and  no  more,  could  find  admission  into 
the  eye. 

Here,  then,  attention  must  be  paid  chiefly  to  the 
aperture  of  the  pupil,  which,  being  variable,  prevents 
our  laying  down  a  fixed  rule,  unless  we  regulate  our- 
selves according  to  a  certain  given  aperture,  which 
is  sufficient,  when  the  pupil,  in  a  state  of  the  greatest 


DEGREE    OF    CLEARNESS.  341 

contraction,  is  filled  with  rays ;  and  for  this  purpose 
the  diameter  of  the  pupil  is  usually  supposed  to  be 
one  line,  twelve  of  which  make  an  inch ;  we  some- 
times satisfy  ourselves  with  even  the  half  of  this, 
allowing  to  the  diameter  of  the  pupil  only  half  aline, 
and  in  some  cases  still  less. 

If  you  will  please  to  consider  that  the  light  of  the 
sun  exceeds  that  of  the  moon  200,000  times,  though 
even  that  of  the  moon  is  hy  no  means  inconsiderable, 
you  will  be  sensible  that  a  small  diminution  in  point 
of  clearness  can  be  of  no  great  consequence  in  the 
contemplation  of  objects.  Having  premised  this,  all 
that  remains  is  to  examine  the  rays  which  the  tele- 
scope transmits  into  the  eye,  and  to  compare  them 
with  the  pupil ;  and  it  will  be  sufficient  to  consider 
the  rays  which  proceed  from  a  single  point  of  the 
object,  that,  for  example,  which  is  in  the  axis  of  the 
telescope. 

1.  The  object  being  infinitely  distant,  the  rays 
which  fall  from  it  on  the  surface  of  the  object-glass 
PAP,  Fig.  180,  are  parallel  to  each  other :  all  the 


Fig.  180. 


rays,  then,  which  come  from  the  centre  of  the  ob- 
ject will  be  contained  within  the  lines  L  P,  L  P, 
parallel  to  the  axis  E  A.  All  these  rays  taken  to- 
gether are  denominated  the  pencil  of  rays  which  fall 
on  the  Object-glass,  and  the  breadth  of  this  pencil  is 
equal  to  the  extent  or  aperture  of  the  object-glass, 
the  diameter  of  which  is  P  A  P. 

2.  This  pencil  of  rays  is  changed  by  the  refrac- 
tion of  the  object-glass  into  a  conical  or  pointed 
figure  P  F  P,  and  having  crossed  at  the  focus  F,  it 
Ff2 


342  DEGREE    OF    CLEARNESS. 

forms  a  new  cone  m  F  m,  terminated  by  the  eye- 
glass ;  hence  it  is  evident  that  the  base  of  this  cone 
mm  is  as  many  times  smaller  than  the  breadth  of 
the  pencil  P  P,  as  the  distance  F  B  is  shorter  than 
the  distance  A  F. 

3.  Now  these  rays  F  m,  F  m,  on  passing  through 
the  eye-glass  Q  B  Q,  become  again  parallel  to  each 
other,  and  form  the  pencil  of  rays  n  o,  n  0,  which 
enter  into  the  eye,  and  there  depict  the  image  of 
the  point  of  the  object  whence  they  originally  pro- 
ceeded. 

4.  The  question,  then,  resolves  itself  into  the 
breadth  of  this  pencil  of  rays  n  o,  n  0,  which  enter 
into  the  eye ;  for  if  this  breadth  n  n  or  o  o  is  equal 
to  or  greater  than  the  opening  of  the  pupil,  it  will 
be  filled  with  them,  and  the  eye  will  enjoy  all  pos- 
sible clearness  ;  that  is,  the  object  will  seem  as  clear 
as  it  you  were  to  look  at  it  with  the  unassisted  eye. 

5.  But  if  this  pencil  nn,  o  o  were  of  much  less 
breadth  than  the  diameter  of  the  pupil,  it  is  evident 
that  the  representation  must  become  so  much  more 
obscure  ;  which  would  be  a  great  defect  in  the  tele- 
scope.    In  order  to  remedy  it,  the  pencil  must  there- 
fore be  at  least  half  a  line  in  breadth ;  and  it  would 
be  still  better  to  have  it  a  whole  line  in  breadth,  this 
being  the  usual  aperture  of  the  pupil. 

6.  It  is  evident  that  the  breadth  of  this  second 
pencil  has  a  certain  relation  to  that  of  the  first,  which 
it  is  very  easy  to  determine.     You  have  only  to 
settle  how  many  times  the  distance  nn  or  mm  is  less 
than  the  distance  P  P,  which  is  the  aperture  of  the 
object-glass.     But  the  distance  P  P  is  in  the  same 
proportion  to  the  distance  m  m,  as  the  distance  A  F 
to  the  distance  B  F,  on  which  the  magnifying  power 
depends ;  accordingly,  the  magnifying  power  itself 
discovers  how  many  times  the  pencil  L  P,  L  P  is 
broader  than  the  pencil  n  o,  n  o,  which  enters  into 
the  eye. 


APERTURE    OF    OBJECT-GLASSES.  343 

7.  Since,  then,  the  breadth  n  n  or  o  o  must  be  one 
line,  at  least  half  a  line,  the  aperture  of  the  object- 
glass  P  P  must  at  least  contain  as  many  half-lines 
as  the  magnifying  power  indicates ;  thus,  when  the 
telescope  is  to  magnify  100  times,  the  aperture  of  its 
object-glass  must  have  a  diameter  of  100  half-lines, 
or  50  lines,  which  make  4  inches  and  2  lines. 

8.  You  see,  then,  that  in  order  to  avoid  obscurity, 
the  aperture  of  the  object-glass  must  be  greater  in 
proportion    as    the  magnifying  power  is  greater. 
And,  consequently,  if  the  object-glass  employed  is 
not  susceptible  of  such  an  aperture,  the  telescope 
will  be  defective  in  respect  of  clearness  of  repre- 
sentation. 

Hence  it  is  abundantly  evident,  that  in  order  to 
magnify  very  greatly  it  is  impossible  to  employ  small 
object-glasses,  whose  focal  distance  is  too  short,  as 
a  lens  formed  by  the  arches  of  small  circles  cannot 
have  a  great  aperture. 

1st  March,  1762. 


LETTER  XCVII. 

Aperture  of  Object-glasses. 

You  have  now  seen  that  the  magnifying  power 
determines  the  size  or  extent  of  the  object-glass, 
in  order  that  objects  may  appear  with  a  sufficient 
degree  of  clearness.  This  determination  respects 
only  the  size  or  aperture  of  the  object-glass  ;  how- 
ever, the  focal  distance  is  affected  by  it  likewise,  for 
the  larger  the  lens  is  the  greater  must  be  its  focal 
distance. 

The  reason  of  this  is  evident,  as  in  order  to  form  a 
lens  whose  focal  distance  is,  for  example,  two  inches, 
its  two  surfaces  must  be  arches  of  a  circle  whose  ra- 
dius is  likewise  about  two  inches.  I  have  therefore 


344  APERTURE    OF    OBJECT-GLASSES. 

represented,  Fig.  181,  two  lenses  P  and  Q, 
the  arches  of  which  are  described  with  a  Fig.  181. 
radius  of  two  inches.  The  lens  P,  being 
the  thicker,  is  much  greater  than  the  lens 
Q  ;  but  I  shall  demonstrate  afterward  that 
thick  lenses  are  subject  to  other  incon-  p[ 
veniences,  and  these  so  great  as  to  oblige 
us  to  lay  them  altogether  aside.  The  lens 
Q,  then,  will  be  found  more  adapted  for 
use,  being  composed  of  smaller  arches  of 
the  same  circle ;  and  as  its  focal  distance  is  two 
inches,  its  extent  or  aperture  m  n  may  scarcely  ex- 
ceed one  inch.  Hence  this  may  be  laid  down  as  a 
general  rule,  that  the  focal  distance  of  a  lens  must 
always  be  twice  greater  than  the  diameter  of  its 
aperture  m  n ;  that  is,  the  aperture  of  a  lens  must 
of  necessity  be  smaller  than  half  the  focal  distance. 

Having  remarked,  then,  that  in  order  to  magnify 
100  times,  the  aperture  of  the  object-glass  must 
exceed  4  inches,  it  follows  that  the  focal  distance 
must  exceed  8  inches  ;  I  shall  presently  demonstrate 
that  the  double  'is  not  sufficient,  and  that  the  focal 
distance  of  this  lens  must  be  increased  beyond  300 
inches.  The  distinctness  of  the  expression  of  the 
image  requires  this  great  increase,  as  shall  afterward 
be  shown :  I  satisfy  myself  with  remarking,  at  pres- 
ent, that  with  regard  to  the  geometrical  figure  of  the 
lens,  the  aperture  cannot  be  greater  than  half  its 
focal  distance. 

Here,  therefore,  I  shall  go  somewhat  more  into 
the  detail  respecting  the  aperture  oT  the  object-glass, 
which  every  magnifying  power  requires ;  and  I  re- 
mark, first,  that  though  a  sufficient  degree  of  clear- 
ness requires  an  aperture  of  four  inches,  when  the 
telescope  is  to  magnify  100  times,  we  satisfy  our- 
selves, in  astronomical  instruments,  with  one  of  three 
inches,  the  diminution  of  clearness  being  scarcely 
perceptible.  Hence  artists  have  laid  it  down  as  a 
rule,  that  in  order  to  magnify  100  times,  the  aperture 


APERTURE    OF    OBJECT-GLASSES.  345 

ot  the  object-glass  must  be  three  inches ;  and  for 
other  magnifying  powers  in  that  proportion.  Thus, 
in  order  to  magnify  50  times,  it  is  sufficient  that  the 
aperture  of  the  object-glass  be  an  inch  and  a  half ; 
to  magnify  25  times,  three-quarters  of  an  inch  suf- 
fice, and  so  of  other  powers. 

Hence  we  see  that  for  small  magnifying  powers  a 
very  small  aperture  of  the  object-glass  is  sufficient, 
and  that,  consequently,  a  moderate  focal  distance 
may  answer.  But  if  you  wished  to  magnify  200 
times,  the  aperture  of  the  object-glass  must  be  six 
inches,  or  half  a  foot,  which  requires  a  very  large 
lens,  whose  focal  distance  must  exceed  even  100  feet, 
in  order  to  obtain  a  distinct  and  exact  expression. 
For  this  reason,  great  magnifying  powers  require 
very  long  telescopes,  at  least  according  to  the  usual 
arrangement  of  lenses  which  I  have  explained.  But 
for  some  time  past  artists  have  been  successfully 
employing  themselves  in  diminishing  this  excessive 
length.  The  aperture  of  the  object-glass,  however, 
must  follow  the  rule  laid  down,  as  clearness  neces- 
sarily depends  on  it. 

Were  you  desirous,  therefore,  of  constructing  a 
telescope  which  should  magnify  400  times,  the  aper- 
ture of  the  object-glass  must  be  twelve  inches,  or  a 
foot,  let  the  focal  distance  be  rendered  as  small  as 
you  will :  and  if  you  wished  to  magnify  4000  times, 
the  aperture  of  the  object-glass  must  be  ten  feet, — a 
very  great  size  indeed,  and  too  much  so  for  any 
artist  to  execute ;  and  this  is  the  principal  reason 
why  we  can  never  hope  to  carry  the  magnifying 
power  so  far,  unless  some  great  prince  would  be  at 
the  expense  of  providing  and  executing  lenses  of 
such  magnitude;  and,  after  all,  perhaps  they  would 
not  succeed. 

A  telescope,  however,  which  should  magnify  4000 
times,  would  discover  many  wonderful  things  in  the 
heavens.  The  moon  would  appear  4000  times  larger 
than  to  the  naked  eye ;  in  other  words,  we  should 


346  APERTURE    OF    OBJECT-GLASSES. 

see  her  as  if  she  were  4000  times  nearer  to  us  than 
she  is.  Let  us  inquire,  then,  to  what  a  degree  we 
might  be  able  to  distinguish  the  different  bodies 
which  she  may  contain.  The  distance  of  the  moon 
from  the  earth  is  calculated  to  be  240,000  English 
miles,  the  4000dth  part  of  which  is  60  miles :  such  a 
telescope  would  accordingly  show  us  the  moon  as 
if  she  were  only  60  miles  distant ;  and,  consequently, 
we  should  be  enabled  to  discover  in  her  the  same 
things  which  we  distinguish  in  objects  removed  to 
the  same  distance.  Now,  from  the  top  of  a  moun- 
tain we  can  easily  discern  other  mountains  more 
than  60  miles  distant.  There  can  be  no  doubt,  then, 
that  with  such  an  instrument  we  should  discover  on 
the  surface  of  the  moon  many  things  to  fill  us  with 
surprise.  But  in  order  to  determine  whether  the 
moon  is  inhabited  by  creatures  similar  to  those  of 
the  earth,  a  distance  of  60  miles  is  still  too  great ; 
we  must  have,  in  order  to  this  effect,  a  telescope 
which  should  magnify  ten  times  more,  that  is  40,000 
times,  and  this  would  require  an  object-glass  of  100 
feet  aperture,  an  enterprise  which  human  art  will 
never  be  able  to  execute.  But  with  such  an  instru- 
ment we  should  see  the  moon  as  if  she  were  no 
farther  distant  than  from  Berlin  to  Spandau,  and 
good  eyes  might  easily  discern  men  at  this  distance, 
if  any  there  were,  but  too  indistinctly,  it  must  be 
allowed,  to  be  completely  assured  of  the  fact. 

As  we  must  rest  satisfied  with  wishing  on  this 
subject,  mine  should  be  to  have  at  once  a  telescope 
which  should  magnify  100,000  times  ;*  the  moon 
would  then  appear  as  if  she  were  only  half  a  mile 
distant. 

The  aperture  of  the  object-glass  of  the  telescope 
must  be  250  feet,  and  we  should  see,  at  least,  the 
larger  animals  which  may  be  in  the  moon. 

6th  March,  1762. 

*  Dr.  Herschel  has  been  able  to  apply  a  magnifying  power  of  6500 
times  to  the  fixed  stars. — Ed. 


ON   DISTINCTNESS   IN   THE    EXPRESSION.      347 


LETTER  XCVIII. 

On  Distinctness  in  the  Expression :  On  the  Space  of  Dif- 
fusion occasioned  by  the  Aperture  of  Object-glasses, 
and  considered  as  the  first  Source  of  Want  of  Dis- 
tinctness in  the  Representation. 

DISTINCTNESS  of  expression  is  a  quality  of  so  much 
importance  in  the  construction  of  telescopes,  that  it 
seems  to  take  precedence  of  all  the  others  which  I 
have  been  endeavouring  to  explain ;  for  it  must  be 
allowed  that  a  telescope  which  does  not  represent 
distinctly  the  images  of  objects  must  be  very  defect- 
ive. I  must  therefore  unfold  the  reasons  of  this 
want  of  distinctness,  that  we  may  apply  more  suc- 
cessfully to  the  means  of  remedying  it. 

They  appear  so  much  the  more  abstruse,  that  the 
principles  hitherto  laid  down  do  not  discover  the 
source  :  in  fact,  this  defect  is  thus  to  be  accounted 
for — one  of  the  principles  on  which  I  have  hitherto 
proceeded  is  not  strictly  true,  though  not  far  from 
the  truth. 

You  will  recollect  that  it  has  been  laid  down  as  a 
principle,  that  a  convex  lens  collects  into  one  point 
of  the  image  all  the  rays  which  come  from  one  point 
of  the  object.  Were  this  strictly  true,  images  rep- 
resented by  lenses  would  be  as  distinctly  expressed 
as  the  object  itself,  and  we  should  be  under  no  ap- 
prehension of  defect  in  regard  to  this. 

Here,  then,  lies  the  defectiveness  of  this  principle ; 
lenses  have  the  property  now  ascribed  to  them  only 
around  their  centre  ;  the  rays  which  pass  through 
the  extremities  of  a  lens  collect  in  a  different  point 
from  those  which  pass  towards  the  centre,  though 
all  proceed  from  the  same  point  of  the  object ;  hence 
are  produced  two  different  images,  which  occasion 
indistinctness. 


348 


ON    DISTINCTNESS    IN 


In  order  to  set  this  in  the  clearest  light,  let  ua 


Fig.  182. 


consider  the  convex  lens 
P  P,  Fig.  182,  on  the  axis 
of  which  is  placed  the  ob- 
ject E  e,  of  which  the  point 

E,  situated  upon  the  axis, 
emits  the  rays  E  N,  E  M, 
E  A,  E  M,  E"N,  to  the  sur- 
face of  the  lens.      To  the 
direction  of  these  rays,  as 
changed  by  refraction,  we 
must  now  pay  attention. 

1.  The   ray  E  A,  which 
passes  through  the  centre 
A  of  the  lens,  undergoes  no 
refraction,  but  proceeds  for- 
ward in  the  same  direction, 
on  the  straight  line  A  B  F. 

2.  The  rays  E  M  and  E  M, 
which  are  nearest  to  the 

first,  undergo  a  small  refraction,  by  which  they  will 
meet  with  the  axis  somewhere  at  F,  which  is  the 
place  of  the  image  F/,  as  has  been  explained  in  some 
of  my  preceding  Letters  on  this  subject. 

3.  The  rays  E  N  and  E  N,  which  are  more  remote 
from  the  axis  E  A,  and  which  pass  towards  the  ex- 
tremities N  N  of  the  lens,  undergo  a  refraction  some- 
what different,  which  collects  them,  not  at  the  point 

F,  but  at  another  point  G,  nearer  the  lens  :  and  these 
rays  represent  another  image  G  g,  different  from  the 
first  F/. 

4.  Let  us  now  carefully  attend  to  this  particular 
circumstance,  not  hitherto  remarked ;  it  is  this,  that 
the  rays  passing  through  the  lens,  towards  its  ex- 
tremities, represent  another  image  G  g,  than  what  is 
represented  by  those  passing  near  the  centre  MAM. 

5.  If  the  rays  E  N,  E  N,  were  to  retire  still  farther 
from  the  centre  A,  and  to  pass  through  the  points 
P  P,  of  the  lens,  their  point  of  reunion  would  be  still 


THE    EXPRESSION.  349 

nearer  to  the  lens,  and  would  form  a  new  image, 
nearer  than  even  G  g. 

6.  Hence  you  will  easily  perceive,  that  the  first 
image  F/,  which  is  named  the  principal  image,  is 
formed  only  by  the  rays  which  are  almost  infinitely 
near  the  centre  ;  and  that  according  as  the  rays  re- 
tire from  it,  towards  the  extremities  of  the  lens,  a 
particular  image  is  formed  nearer  the  lens,  till  those 
passing  close  to  the  extremities  form  the  last,  G  g. 

7  All  the  rays,  therefore,  which  pass  through  the 
lens  P  P  represent  an  infinity  of  images  disposed 
between  F/  and  G  g;  and  at  every  distance  from 
the  axis  the  refraction  of  the  lens  produces  a  par- 
ticular image,  so  that  the  whole  space  between  F  and 
G  is  filled  with  a  series  of  images. 

8.  This  series  of  images  is  accordingly  denomi- 
nated the  diffusion  of  the  image  ;  and  when  all  these 
rays  afterward  enter  into  an  eye,  it  is  natural  that 
the  vision  should  be  so  much  disturbed  as  the  space 
F  G,  through  which  the  image  is  diffused,  is  more 
considerable.     If  this  space  F  G  could  be  reduced  to 
nothing,  no  confusion  need  be  apprehended. 

9.  The  greater  portions  of  their  respective  circles 
that  the  arches  PAP  and  P  B  P  are,  the  greater 
likewise  is  F  G  the  space  of  diffusion.     You  see  a 
good  reason,  then,  for  rejecting  all  lenses  of  too 
great  thickness,  or  in  which  the  arches  which  form 
the  surfaces  of  the  lens  are  considerable  segments 
of  their  circles,  as  in  Fig.  183,  of  which 

the  arches  PAP  and  P  B  P  are  the  fourth  Fig.  183. 
part  of  the  whole  circumference,  so  that 
each  contains  90°  ;    this  would,  conse- 
quently produce  an  insufferable  confusion. 

10.  The  arches,  then,  which  form  the 
surfaces  of  a  lens,  must  contain  much 
less  than  90  degrees :  if  they  contained 
so  much  as  60,  the  diffusion  of  the  image 
would  be  even  then  insupportable.     Au- 
thors who  have  treated  the  subject  admit 

VOL.  II.— G  g 


350       ON    DISTINCTNESS    IN   THE    EXPRESSION. 

of  30  degrees  at  most :   and  some  fix  the  „.     lft , 
boundary  at  20  degrees.     A  lens  of  this  last     #* 
description  is  represented  by  Fig-.  184,  in 
which  the  arches  PAP  and  P  B  P  contain 
only  20  degrees,  each  being  but  the  eigh- 
teenth part  of  the  whole  circumference  of 
its  respective  circle. 

11.  But  if  this  lens  were  to  supply  the 
place  of  the  object-glass  in  a  telescope,  the 

arches  PAP  and  P  B  P  must  contain  still  many 
degrees  less.  For  though  the  diffusion  of  the  image 
be  perceptible  of  itself,  the  magnifying  power  mul- 
tiplies it  as  many  times  as  it  does  the  object.  There- 
fore, the  greater  the  magnifying  power  proposed, 
the  fewer  must  be  the  number  of  degrees  which 
the  surfaces  of  the  lens  contain. 

12.  When  the  telescope  is  intended  to  magnify 
100  times,  you  will  recollect  that  the  aperture  of 
the  object-glass  must  be  3  inches,  and  its  focal  dis- 
tance 360  inches,  which  is  equal  to  the  radii  witft 
which  the  two  arches  PAP  and  P  B  P  are  described ; 
hence  it  follows  that  each  of  these  two  arches  con- 
tains but  half  a  degree  ;  and  it  is  distinctness  of  ex- 
pression which  requires  an  arch  so  small.     If  it 
were  intended  to  magnify  200  times,  half  a  degree 
would  be  still  too  much,  and  the  measure  of  the  arch, 
in  that  case,  ought  not  to  exceed  the  third  part  of  a 
degree.     This  arch,  however,  must  receive  an  extent 
of  6  inches  ;  the  radius  of  the  circle  must  therefore 
be  so  much  greater,  and  consequently  also  the  focal 
distance.     This  is  the  true  reason  why  great  magni- 
fying powers  require  telescopes  of  such  considerable 
length. 

Qth  March,  1762 


APERTURE    OF   LENSES.  351 


LETTER  XCIX. 

Diminution  of  the  Aperture  of  Lenses,  and  other  means 
of  lessening  the  Space  of  Diffusion  till  it  is  reduced 
to  nothing. 

WHEN  the  space  of  an  object-glass  is  too  great  to 
admit  of  distinctness  of  expression,  it  may  be  very 
easily  remedied :  you  have  only  to  cover  the  lens 
with  a  circle  of  pasteboard,  leaving  an  opening  in  the 
centre,  so  that  the  lens  may  transmit  no  other  rays 
but  those  which  fall  upon  it  through  the  opening, 
and  that  those  which  before  passed  through  the  ex- 
tremities of  the  lens  may  be  excluded  ;  for  as  no  rays 
are  transmitted  but  through  the  middle  of  the  lens, 
the  smaller  the  opening  is  the  smaller  likewise  will 
be  the  space  of  diffusion.  Accordingly,  by  a  gradual 
diminution  of  the  opening,  the  space  of  diffusion  may 
be  reduced  at  pleasure. 

Here  the  case  is  the  same  as  if  the  lens  were  no 
larger  than  the  opening  in  the  pasteboard,  thus  the 
covered  part  becomes  useless,  and  the  opening  de- 
termines the  size  of  the  lens ;  this  then  is  the  remedy 
employed  to  give  object-glasses  any  given  extent. 

P  P  is  the  object-glass,  Fig.  185,  before 
which  is  placed  the  pasteboard  N  N,  having 
the  opening  M  M,  which  is  now  the  extent 
of  the  lens.     This  opening  M  M  is  here 
nearly  the  half  of  what  it  would  be  were 
the  pasteboard  removed  ;  the  space  of  dif- 
fusion is  therefore  much  smaller.     It  is 
remarked,  that  the  space  of  diffusion  in 
this  case  is  only  the  fourth  part  of  what 
it  was  before.     An  opening  M  M,  reduced  to  a  third 
of  P  P,  would  render  the  space  of  diffusion  nine 
times  less.     Thus  the  effect  of  this  remedy  is  very 
considerable ;  and  on  covering  the  extremities  of 


352  DIMINUTION    OF   THE 

the  lens  ever  so  little,  the  effect  of  it  becomes  per- 
ceptible. 

If,  therefore,  a  telescope  labours  under  this  defect, 
that  it  does  not  represent  objects  sufficiently  distinct, 
as  a  series  of  images  blended  tog-ether  must  of  ne- 
cessity produce  confusion,  you  have  only  to  con- 
tract the  aperture  of  the  object-glass  by  a  covering 
of  pasteboard  such  as  I  have  described,  and  this 
confusion  will  infallibly  disappear.  But  a  defect 
equally  embarrassing  is  the  consequence  ;  the  de- 
gree of  brightness  is  diminished.  You  will  recollect 
that  every  degree  of  the  magnifying  power  requires 
a  certain  aperture  of  the  object-glass,  that  as  many 
rays  may  be  transmitted  as  are  necessary  to  procure 
a  sufficient  illumination.  It  is  vexatious,  therefore, 
in  curing  one  defect,  to  fall  into  another;  and  in 
order  to  the  construction  of  a  very  good  telescope, 
it  is  absolutely  necessary  that  there  should  be  suffi- 
cient brightness  of  illumination,  without  injuring 
distinctness  in  the  representation. 

But  can  there  be  no  method  of  diminishing,  nay, 
of  totally  reducing  the  space  of  diffusion  of  object- 
glasses  without  diminishing  the  aperture  1  This  is 
the  great  inquiry  which  has  for  some  time  past  en- 
gaged the  attention  of  the  ingenious,  and  the  solution 
of  which  promises  such  a  field  of  discovery  in  the 
science  of  dioptrics.  I  shall  have  the  honour,  at 
least,  of  laying  before  you  the  means  which  scientific 
men  have  suggested  for  this  purpose. 

As  the  focus  of  the  rays  which  pass  through  the 
middle  of  a  convex  lens  is  more  distant  from  the 
lens  than  the  focus  of  the  rays  which  pass  through 
the  extremities,  it  has  been  remarked  that  concave 
lenses  produce  a  contrary  effect.  This  has  sug- 
gested the  inquiry,  whether  it  might  not  be  possible 
to  combine  a  convex  with  a  concave  lens,  in  such  a 
manner  that  the  space  of  diffusion  should  be  entirely 
annihilated ;  while,  in  other  respects,  this  compound 
lens  should  produce  the  same  effect  as  an  ordinary 


APERTURE    OF    LENSES. 


353 


simple  object-glass  1  You  know  that  concave  lenses 
are  measured  by  their  focal  distance  as  well  as  those 
which  are  convex;  with  this  difference,  that  the 
focus  of  the  concave  is  only  imaginary,  and  falls  be- 
fore the  lens,  whereas  the  focus  of  convex  lenses  is 
real,  and  falls  behind  them.  Having  made  this  re- 
mark, we  reason  as  follows  : 

1.  If  we  place,  Fig.  186,  behind  a  con- 
vex lens  P  A  P,  a  concave  one  Q  B  Q  of 
the  same  focal  distance,  the  rays  which 
the  convex  lens  would  collect  in  its  focus 
will  be  refracted  by  the  concave,  so  that 
they  will  again  become  parallel  to  each 
other,  as  they  were  before  passing  through 
the  convex  lens. 

2.  In  this  case,  therefore,  the  concave 
lens  destroys  the  effect  of  the  convex,  and 

it  is  the  same  thing  as  if  the  rays  had  proceeded  in 
their  natural  direction,  without  undergoing  any  re- 
fraction. For  the  concave  lens,  having  its  focus  at 
the  same  point  F  (see  Fig.  178,  p.  331),  restores  the 
parallelism  of  the  rays,  which  would  otherwise  have 
met  at  the  point  F. 

3.  If  the  focal  distance  of  the  concave  lens  were 
smaller  than  that  of  the  convex,  it  would 
produce  a  greater  effect,  and  would  ren-   Fig.  187. 
der  the  rays  divergent,  as  in  Fig.  187  :  the 
incident  parallel  rays  L  M,  E  A,  L  M,  pass- 
ing through  the  two  lenses,  would  assume 

the  directions  NO,  B  F,  N  0,  which  are 
divergent  from  each  other.  These  two 
lenses  together  produce,  therefore,  the 
same  effect  as  a  simple  concave  lens, 
which  would  impress  on  the  incident  par- 
allel rays  the  same  divergence.  Two 
such  lenses  joined  together,  of  which  the 
concave  has  a  smaller  focal  distance  than 
the  convex,  are  therefore  equivalent  to  a 
simple  concave  lens. 

Gg2 


354 


APERTURE    OF    LENSES. 


Fig,  188 


4.  But  if  the  concave  lens  Q  Q,  Fig. 
188,  has  a  greater  focal  distance  than 
the  convex  lens  P  P,  it  is  not  even  suf- 
ficient to  render  parallel  to  each  other 
the  rays  which  the  convex  lens  by  it- 
self would  collect  in  its  focus  F :  these 
rays,  therefore,  continue  convergent, 
but  their  convergence  will  be  dimin- 
ished by  the  concave  lens,  so  that  the     . 
rays,  instead  of  meeting  in  the  point  F, 
will  meet  in  the  more  distant  point  O. 

5.  These  two  lenses  joined  together 
will  produce,  then,  the  same  effect  as 
a  simple  convex  lens  which  should 
have  its  focus  at  0,  as  it  would  collect 
the  parallel  rays  L  M,  E  A,  L  M,  equally 
in  the  same  point.     It  is  therefore  evi- 
dent that  two  lenses  may  be  combined 

an  infinite  variety  of  ways,  the  one  being  convex  and 
the  other  concave,  so  that  their  combination  shall  be 
equivalent  to  a  given  convex  lens. 

6.  Such  a  double  object-glass  may  therefore  be 
employed  in  the  construction  of  telescopes,  instead 
of  the  simple  one,  to  which  it  is  equivalent ;  and  the 
effect  as  to  the  magnifying  power  will  be  just  the 
same.     But  the  space  of  diffusion  will  be  quite  dif- 
ferent, and  it  may  happen  to  be  greater  or  less  than 
that  of  a  simple  object-glass ;  and  in  this  last  case 
the  double  object-glass  will  be  greatly  preferable  to 
the  simple  one. 

7.  But,  further,  it  has  been  found  possible  to  ar- 
range two  such  lenses  so  that  the  space  of  diffusion 
is  reduced  absolutely  to  nothing,  which  is  undoubt- 
edly the  greatest  advantage  possible  in  the  construc- 
tion of  telescopes.     Calculation  enables  us  to  deter- 
mine this  arrangement,  but  no  artist  has  hitherto 
been  found  capable  of  reducing  it  to  practice. 

I3lh  March,  1762. 


OF   COMPOUND    OBJECT-GLASSES.  355 

LETTER  C. 

Of  Compound  Object-glasses. 

THE  combination  of  two  lenses,  of  which  I  have 
now  given  the  idea,  is  denominated  a  compound 
object-glass ;  the  end  proposed  from  them  is,  that 
all  the  rays,  as  well  those  which  pass  through  the 
extremities  of  a  lens  as  those  which  pass  through 
the  middle,  should  be  collected  in  a  single  point,  so 
that  only  one  image  may  be  formed,  without  diffu- 
sion, as  in  simple  object-glasses.  Could  artists 
succeed  in  effecting  such  a  construction,  very  great 
advantages  would  result  from  it,  as  you  shall  see. 

It  is  evident,  first,  that  the  representation  of  ob- 
jects must  be  much  more  distinct,  and  more  exactly 
expressed,  as  vision  is  not  disturbed  by  the  appari- 
tion of  that  series  of  images  which  occupy  the  space 
of  diffusion  when  the  object-glass  is  simple. 

Again,  as  this  space  of  diffusion  is  the  only  reason 
which  obliges  us  to  give  to  simple  object-glasses 
such  an  excessive  focal  distance,  in  order  to  render 
the  inconvenience  resulting  from  it  imperceptible,  by 
employing  compound  object-glasses  we  are  relieved 
from  that  cumbersome  expedient,  and  are  enabled 
to  construct  telescopes  incomparably  shorter,  yet 
possessing  the  same  magnifying  power. 

When,  employing  a  single  object-glass,  you  want 
to  magnify  a  hundred  times,  the  focal  distance  can- 
not be  less  than  thirty  feet,  and  the  length  of  the 
telescope  becomes  still  greater  on  account  of  the 
eye-glass,  whose  focal  distance  must  be  added;  a 
small  object-glass  would  produce,  from  its  greater 
space  of  diffusion,  an  intolerable  confusion.  But  a 
length  of  thirty  feet  is  not  only  very  incommodious, 
but  artists  seldom  succeed  in  forming  lenses  of  so 
great  a  focal  distance.  You  will  readily  perceive 


356  OF    COMPOUND   OBJECT-GLASSES. 

the  reason  of  this  ;  for  the  radius  of  the  surfaces  of 
such  a  lens  must  likewise  be  thirty  feet,  and  it  is 
very  difficult  to  describe  exactly  so  great  a  circle, 
and  the  slightest  aberration  renders  all  the  labour 
useless. 

Accidents  of  this  sort  are  not  to  be  apprehended 
in  the  construction  of  compound  object-glasses, 
which  may  be  formed  of  smaller  circles,  provided 
they  are  susceptible  of  the  aperture  which  the  mag- 
nifying power  requires.  Thus,  in  order  to  magnify 
one  hundred  times,  we  have  seen  that  the  aperture 
of  the  object-glass  must  be  three  inches ;  but  it  would 
be  easy  to  construct  a  compound  object-glass  whose 
focal  distance  should  be  only  one  hundred  inches, 
and  which  could  admit  an  aperture  of  more  than 
three  inches  :  therefore,  as  the  focal  distance  of  the 
eye-glass  must  be  one  hundred  times  smaller,  it  would 
be  one  inch ;  and  the  interval  between  the  lenses 
being  the  sum  of  their  focal  distances,  the  length  of 
the  telescope  would  be  only  one  hundred  and  one 
inches,  or  eight  feet  five  inches,  which  is  far  short 
of  thirty  feet. 

But  it  appears  to  me  that  a  compound  object-glass, 
whose  focal  distance  should  be  fifty  inches,  might 
easily  admit  an  aperture  of  three  inches,  and  even 
more  :  taking,  then,  an  eye-glass  of  half  an  inch 
focus,  you  will  obtain  the  same  magnifying  power  of 
one  hundred  times,  and  the  length  of  the  telescope 
will  be  reduced  one-half,  that  is,  to  four  feet  and  less 
than  three  inches.  Such  a  telescope,  then,  would 
produce  the  same  effect  as  a  common  one  of  thirty 
feet,  which  is  assuredly  carrying  it  as  far  as  need 
be  wished. 

If  such  a  compound  object-glass  could  be  made  to 
answer,  you  would  only  have  to  double  all  these 
measurements  in  order  to  have  one  which  should 
admit  an  aperture  of  six  inches ;  and  this  might  be 
employed  to  magnify  two  hundred  times,  making  use 
of  an  eye  glass  of  half  an  inch  focus  as  the  two  mm- 


OF    COMPOUND    OBJECT-GLASSES.  357 

dredth  part  of  the  focal  distance  of  the  object-glass, 
which  would,  in  this  case,  be  one  hundred  inches. 
Now,  a  common  telescope  which  should  magnify  two 
hundred  times,  must  exceed  one  hundred  feet  in 
length ;  whereas  this  one,  which  is  constructed  with 
a  compound  object-glass,  is  reduced  to  about  eight 
feet,  and  is  perfectly  accommodated  to  use,  whereas 
a  telescope  of  one  hundred  feet  long  would  be  an 
unwieldly  and  almost  useless  load. 

The  subject  might  be  carried  still  much  further, 
and  by  again  doubling  the  measurements,  we  might 
have  a  compound  object-glass  whose  focal  distance 
should  be  two  hundred  inches,  or  sixteen  feet  eight 
inches,  which  should  admit  of  an  aperture  of  twelve 
inches,  or  one  foot :  taking,  then,  an  eye-glass  of 
half  an  inch  focus,  as  two  hundred  inches  contain 
four  hundred  half-inches,  we  should  have  a  telescope 
capable  of  magnifying  four  hundred  times,  and  still 
abundantly  manageable,  being  under  seventeen  feet; 
whereas,  were  we  to  attempt  to  produce  the  same 
magnifying  power  with  a  simple  object-glass,  the 
length  of  the  telescope  must  exceed  three  hundred 
feet,  and  consequently  could  be  of  no  manner  of  use 
on  account  of  that  enormous  size. 

They  have  at  Paris  a  telescope  one  hundred  and 
twenty  feet  long,  and  one  at  London  of  one  hundred 
and  thirty  feet ;  but  the  dreadful  trouble  of  mount- 
ing and  pointing  them  to  the  object  almost  annihi- 
lates the  advantages  expected  from  them.  From 
this  you  will  conclude  of  what  importance  it  would 
be  to  succeed  in  the  construction  of  the  compound 
lenses  which  I  have  been  describing.  I  suggested 
the  first  idea  of  them  several  years  ago,  and  since 
then  artists  of  the  greatest  ability  in  England  and 
France  have  been  attempting  to  execute  them. 
Repeated  efforts  and  singular  skill  in  the  artist  are 
undoubtedly  requisite.  Indeed,  I  have  made,  with 
the  assistance  of  an  able  mechanician  of  our  Acade- 
my, some  not  unsuccessful  attempts ;  but  the  ex- 


358  FORMATION   OF 

pense  attending  such  an  enterprise  has  obliged  me 
to  give  it  up. 

But  the  Royal  Society  of  London  last  year  an- 
nounced, that  an  eminent  artist,  of  the  name  of  Dol- 
lond*  had  fortunately  succeeded ;  and  his  telescopes 
are  now  universally  admired.  An  able  artist  of 
Paris,  named  Passement,  boasts  of  a  simitar  success. 
Both  these  gentlemen  did  me  the  honour,  some 
time  ago,  to  correspond  with  me  on  the  subject ;  but 
as  the  point  in  question  was  chiefly  how  to  surmount 
certain  great  difficulties  in  the  practical  part,  which  I 
never  attempted,  it  is  but  fair  that  I  should  relinquish 
to  them  the  honour  of  the  discovery.  The  theory 
alone  is  my  province,  and  it  has  cost  me  much  pro- 
found research,  and  many  painful  calculations,  the 
very  sight  of  which  would  terrify  you.  I  shall 
therefore  take  care  not  to  perplex  you  further  with 
this  abstruse  inquiry. 

16th  March,  1762. 


LETTER  CI 

Formation  of  Simple  Object-glasses. 

IN  order  to  give  you  some  idea  of  the  researches 
which  led  me  to  the  construction  of  compound  ob- 
ject-glasses, I  must  begin  with  the  formation  of  the 
simple  lens. 

Observe,  first,  that  the  two  surfaces  of  a  lens  may 
be  formed  in  an  infinity  of  different  ways,  by  taking 
circles  of  which  the  surfaces  are  segments,  either 
equal  or  unequal  to  each  other,  the  focal  distance, 
however,  remaining  always  the  same. 

*  The  first  achromatic  telescope  ever  constructed  was  made  by  Chester 
More  Hall,  Esq.,  of  More-hall,  in  Essex,  in  thu  year  1733.  no  less  than 
twei'ty-four  years  before  the  period  alluded  to  by  our  author.  This  in- 
valuable instrument,  is,  therefore,  in  every  view  of  the  matter,  a  British 
invention.  See  the  article  Optics,  in  the  Edinburgh  Encyclopaedia,  vol. 
XV.  p.  479,  note,  for  a  full  account  of  Mr-  Hall's  labours.— Ed. 


SIMPLE    OBJECT-GLASSES.  359 

The  same  figure  is  usually  given  to  both  surfaces 
of  a  lens,  or,  as  the  surfaces  of  a  lens  are  repre- 
sented by  arches  of  a  circle,  both  surfaces  are  formed 
with  radii  equal  to  each  other.  Facility  of  execu- 
tion has  undoubtedly  recommended  this  figure,  as 
the  same  basin  serves  to  form  both  surfaces,  and 
most  artists  are  provided  with  but  few  basins. 

Suppose,  then,  a  convex  lens,  both  whose  surfaces 
are  polished  on  the  same  basin,  one  of  twenty-four 
inches  radius,  so  that  each  surface  shall  be  an  arch  of 
the  circle  whose  radius  is  twenty-four  inches  :  this 
lens  will  be  convex  on  both  sides,  and  will  have  its 
focal  distance  at  twenty-four  inches,  according  to 
the  common  calculation ;  but  as  the  focus  depends 
on  the  refraction,  and  as  the  refraction  is  not  abso- 
lutely the  same  in  every  species  of  glass,  in  which  we 
find  a  very  considerable  diversity,  according  as  the 
glass  is  more  or  less  white  and  hard,  this  calculation 
of  the  focus  is  not  strictly  accurate  ;  and  usually  the 
focal  distance  of  the  lens  is  somewhat  less  than  the 
radius  of  its  two  surfaces,  sometimes  the  tenth 
part,  sometimes  the  twelfth :  accordingly,  the  sup- 
posed lens,  the  radius  of  whose  surfaces  is  twenty- 
four  inches,  will  have  its  focus  at  the  distance  of 
about  twenty-two  inches,  if  it  is  formed  of  the  same 
species  of  glass  of  which  mirrors  are  commonly 
manufactured  ;  though  even  in  glass  of  this  sort  we 
meet  with  a  small  diversity  in  respect  of  refraction. 

We  see  afterward,  that  on  making  the  two  sur- 
faces of  the  lens  unequal,  an  infinity  of  other  lenses 
may  be  formed,  which  shall  all  have  the  same  focal 
distance  ;  for  on  taking  the  radius  of  one  of  the 
surfaces  less  than  twenty-four  inches,  that  of  the 
other  surface  must  be  taken  greater  in  proportion, 
according  to  a  certain  rule.  The  radius  of  one  of 
the  surfaces  may  always  be  taken  at  pleasure  ;  and 
by  means  of  a  certain  rule  the  radius  of  the  other 
may  be  found,  in  order  that  the  focal  distance  may 
become  the  same  as  if  each  surface  had  been  formed 


360  FORMATION    OF 

on  a  radius  of  twenty-four  inches.  The  following 
table  exhibits  several  such  lenses,  which  have  all 
the  same  focal  distance. 

Lenses.  Radius  of  the  first  Surface.  Radius  of  the  Second  Surface* 
I.                    24  24 

II.  21  28 

III.  20  30 

IV.  18  36 
V.              -     16                                    48 

VI.  15  60 

VII.  14  84 

VIII.  13  156 

IX.  12  infinity 

In  the  last  form,  the  radius  of  one  surface  is  only 
12  inches,  or  the  half  of  24  inches  ;  but  that  of  the 
other  becomes  infinite :  or  rather,  this  surface  is  an 
arch  of  a  circle  infinitely  great ;  and  as  such  an  arch 
differs  nothing  from  a  straight  line,  this  may  be  con- 
sidered as  a  plane  surface,  and  such  a  lens  is  plano- 
convex. 

Were  we  to  assume  the  radius  of  a  surface  still 
smaller  than  12  inches,  the  other  surface  must  be 
made  concave,  and  the  lens  will  become  convexo- 
concave;  it  will,  in  that  case,  bear  the  name  of 
meniscus,  several  figures  of  which  are  represented 
in  the  following  table : — 

Meniscus.        Radius  of  the  Convex          Radius  of  the  Concave 
Surface.  Surface. 

X.  11  132 

XI.  10  60 

XII.  9  36 

XIII.  8  24 

XIV.  6  12 
XV.  4  6 

XVI.  3  4 

Here,  then,  is  a  new  species  of  lenses,  the  last  of 


SIMPLE    OBJECT-GLASSES.  361 

which  is  represented  in  Fig.  190,  so  that  p-     ^Q 
we  have  now  sixteen  different  species,      **-- — ' 
which  have  all  the  same  focal  distance  ;    k* ^ 
and  this  is  about  22  inches,  a  little  more 
or  less,  according  to  the  nature  of  the  glass. 

When,  therefore,  the  only  question  is,  What  focal 
distance  the  lens  ought  to  have  \  it  is  a  matter  of 
indifference  according  to  which  of  these  forms  you 
go  to  work  ;  but  there  may  be  a  very  great  differ- 
ence in  the  space  of  diffusion  to  which  each  species 
is  subjected,  this  space  becoming  smaller  in  some 
than  in  others.  When  a  simple  object-glass  is  to 
be  employed,  as  is  usually  done,  it  is  by  no  means 
indifferent  of  what  figure  you  assume  it,  for  that 
which  produces  the  smallest  space  of  diffusion  is 
to  be  preferred.  Now,  this  excellent  property  does 
not  belong  to  the  first  species,  where  the  two  sur- 
faces are  equal;  but  nearly  to  species  VII.,  which 
possesses  the  quality,  that  when  you  turn  towards 
the  object  its  more  convex  surface,  or  that  whose 
radius  is  smallest,  the  space  of  diffusion  is  found  to 
be  about  one-half  less  than  when  the  lens  is  equally 
convex  on  both  sides :  this,  therefore,  is  the  most 
advantageous  figure  for  simple  object-glasses,  and 
practitioners  are  accordingly  agreed  in  the  use  of  it. 

It  is  evident,  then,  that  in  order  to  ascertain  the 
space  of  diffusion  of  a  lens,  it  is  not  sufficient  to 
know  its  focal  distance ;  its  species  likewise  must 
be  determined,  that  is,  the  radii  of  each  surface ;  and 
you  must  carefully  distinguish  which  side  is  turned 
to  the  object. 

After  this  explanation,  it  is  necessary  to  remark, 
that  in  order  to  discover  the  combination  of  two 
lenses  which  shall  produce  no  diffusion  of  image, 
it  is  absolutely  necessary  to  take  into  the  account 
the  figure  of  both  surfaces  of  each  glass,  and  to 
resolve  the  following  problem:  What  must  be  the 
radii  of  the  surfaces  of  two  lenses,  in  order  to  reduce 
to  nothing  the  space  of  diffusion  ?  The  solution  re- 

VOL.  II.— H  h 


362  DEFECT   OF    REPRESENTATION 

quires  the  most  profound  researches  of  the  most 
sublime  geometry;  and  supposing  these  to  have 
been  successful,  the  artist  has,  after  all,  many  diffi- 
culties to  surmount.  The  basins  must  have  pre- 
cisely that  curve  which  the  calculation  indicates; 
nor  is  that  sufficient,  for  in  the  operation  of  forming 
the  lens  on  the  basin,  the  basin  suffers  from  the 
friction  in  its  turn ;  hence  it  becomes  necessary  to 
rectify  its  figure  from  time  to  time,  with  all  possible 
accuracy,  for  if  all  these  precautions  are  not  strictly 
observed,  it  is  impossible  to  ensure  success  ;  and  it 
is  no  easy  matter  to  prevent  the  lens  from  assuming 
a  figure  somewhat  different  from  that  of  the  basin 
in  which  it  is  moulded.  You  must  be  sensible,  from 
all  this,  how  difficult  it  must  be  to  carry  to  perfec 
tion  this  important  article  in  dioptrics. 
2Qth  March,  1762. 


LETTER  GIL 

Second  Source  of  Defect  as  to  Distinctness  of  Represent- 
ation by  the  Telescope.  Different  Refrangibility  of 
Rays. 

You  have  now  seen  in  what  manner  it  may  be 
possible  to  remedy  that  defect  in  lenses  which  arises 
from  the  different  refraction  of  rays,  as  those  which 
pass  through  the  extremities  of  a  lens  do  not  meet 
in  the  same  point  with  those  which  pass  through  its 
middle,  the  effect  of  which  is  an  infinity  of  images 
dispersed  through  the  space  of  diffusion.  But  this 
is  not  the  only  defect ;  there  is  another,  of  so  much 
more  importance  that  it  seems  impossible  to  apply 
a  remedy,  as  the  cause  exists,  not  in  the  glass,  but 
in  the  nature  of  the  rays  themselves. 

You  will  recollect  that  there  is  a  great  variety  in 
rays,  with  respect  to  the  different  colours  of  which 
they  convey  the  impression.  I  have  compared  this 


BY    THE    TELESCOPE.  363 

diversity  to  that  which  we  meet  with  in  musical 
notes,  having  laid  it  down  as  a  principle,  that  each 
colour  is  attached  to  a  certain  number  of  vibrations. 
But  supposing  that  this  explanation  should  still  ap- 
pear doubtful,  it  is  beyond  all  doubt  that  rays  of 
different  colours  likewise  undergo  different  refrac- 
tions in  their  passage  from  one  transparent  medium 
to  another ;  thus,  red  rays  undergo  the  least  refrac- 
tion, and  violet  the  greatest,  though  the  difference 
is  almost  imperceptible.  Now,  all  the  other  colours, 
as  orange,  yellow,  green,  and  blue,  are  contained, 
with  respect  to  refraction,  within  these  two  limits. 
It  must  likewise  be  remarked,  that  white  is  a  mix- 
ture of  all  the  colours  which  by  refraction  are  sepa- 
rated from  each  other. 

In  fact,  when  a  white  ray  0  P,  Fig.  191,  or  a  ray 
of  the  sun,  falls  obliquely  on  jVo-.  191. 

a  piece  of  glass  ABC  D, 
instead  of  pursuing  its  course 
in  the  direction  P  Q,  it  not 

only  deviates  from  this,  but  A        \p B 

divides  into  a  variety  of  rays,  t\ 

P  r,  P  s,  P  t,  P  v  :  the  first  |V\ 

of  which  P  r,  the  one  that  _ i\\\  \ 

deviates  least,  represents  c 
the  red  colour,  and  the  last  P  »,  which  deviates 
most,  the  violet  colour.  The  dispersion  r  v  is  in- 
deed much  smaller  than  it  appears  in  the  figure ; 
the  divergence,  however,  always  becomes  more 
perceptible. 

From  this  different  refrangibility  of  rays,  accord- 
ing to  their  different  colours,  are  produced  the  fol- 
lowing phenomena  with  respect  to  dioptric  glasses  : 

1.  Let  P  P,  Fig.  192,  be  a  convex  lens,  on  the 
axis  of  which  O  R,  at  a  very  great  distance  A  O,  is 
the  object  O  o,  the  image  of  which,  as  represented 
by  the  lens,  we  are  to  determine, 'putting  aside  here 
the  first  irregularity,  that  which  respects  diffusion; 
or,  which  amounts  to  the  same  thing,  attending 


364  DEFECT    OF    REPRESENTATION 

to  those  rays  only  which  pass  through    Fig.  192. 
the  centre  of  the  lens  A  B,  as  if  its  ex- 
tremities  were  covered  with  a  circle  of 
pasteboard. 

2.  Let  us  now  suppose  the  object  O  o 
to  be  red,  so  that  all  its  rays  shall  be  of 
the  same  nature;  the  lens  will  some- 
where represent  the  image  of  it  R  r 
equally  red  ;  the  point  R  is,  in  this  case, 
denominated  the  focus  of  the  red  rays, 
or  of  those  which  undergo  the  least  re- 
fraction. 

3.  But  if  the  object  0  o  is  violet,  as 
rays  of  this  colour  undergo  the  greatest 
refraction,  the  image  V  v  will  be  nearer 
the  lens  than  R  r ;  this  point  v  is  called 
the  focus  of  violet  rays. 

4.  If  the  object  were  painted  some  other  inter- 
mediate colour  between  red  and  violet,  the  image 
would  fall  between  the   points  R  and  V,  would 
be   always  very  distinct,   and  terminated  by  the 
straight  line  o  B,  drawn  from  the  extremity  o  of  the 
object,  through  the  centre  of  the  lens,  this  being  a 
general  rule  for  all  colours. 

5.  But  if  the  colour  of  the  object  is  not  pure,  as 
is  the  case  in  almost  all  bodies,  or  if  the  object  is 
white,  which  is  a  mixture  of  all  colours,  the  differ- 
ent species  of  rays  will  then  be  separated  by  refrac- 
tion, and  each  will  represent  an  image  apart.     That 
which  is  formed  of  red  rays  will  be  at  R  r ;  and  that 
which  is  produced  by  the  violet  at  V  v ;  and  the 
whole  space  R  V  will  be  filled  with  images  of  the 
intermediate  colours. 

6.  The  lens  P  P,  then,  will  represent  a  succession 
of  images  of  the  object  O  o,  disposed  through  the 
small  space  R  V,  of  which  the  most  remote  from 
the  lens  is  red,  and  the  nearest  V  v  violet,  and  the 
intermediate  images  of  the  intermediate  colours, 


BY    THE    TELESCOPE.  365 

according  to  the  order  of  the  colours  as  they  appear 
in  the  rainbow. 

7.  Each  of  these  images  will  be  abundantly  dis- 
tinct in  itself,  and  all  terminated  by  the  straight  line 
o  B  v  r,  drawn  from  the  extremity  o  of  the  object 
through  the  centre  of  the  lens  B ;  but  they  could 
not  be  viewed  together  \vithout  a  very  perceptible 
confusion. 

8.  Hence,  then,  is  produced  a  new  space  of  dif- 
fusion, as  in  the  first  irregularity ;  but  differing  from 
it  in  this — that  the  latter  is  independent  on  the  aper- 
ture of  the  lens,  and  that  each  image  is  painted  of  a 
particular  colour. 

9.  This  space  of  diffusion  R  V  depends  on  the 
focal  distance  of  the  lens,  so  as  to  be  always  about 
the  28th  part ;  when,  therefore,  the  focal  distance 
of  the  lens  P  P  is  28  feet,  the  space  R  V  becomes 
equal  to  an  entire  foot,  that  is,  the  distance  between 
the  red  image  R  r  and  the  violet  V  v  is  one  foot, 
If  the  focal  distance  were  twice  as  great,  or  56  feet, 
the  space  R  V  would  be  two  feet ;  and  so  of  other 
distances. 

10.  Hence  the  calculation  of  the  focal  distance  of 
a  lens  becomes  uncertain,  as  the  rays  of  each  colour 
have   their  separate   focus ;   when,  therefore,   the 
focus  of  a  lens  is  mentioned,  it  is  always  necessary 
to  announce  the  colour  that  we  mean.     But  rays  of 
an  intermediate  nature  are  commonly  understood, 
those  between  red  and  violet,  namely  the  green. 

11.  Thus,  when   it  is  said,  without  further  ex- 
planation, that  the  focal  distance  of  such  a  lens  is 
56  feet,  we  are  to  understand  that  it  is  the  green 
image  which  falls  at  that  distance  ;  the  red  image 
will  fall  about  a  foot  farther  off,  and  the  violet  a  foot 
nearer. 

Here,  then,  is  a  new  circumstance  of  essential 
importance,  to  which  attention  must  be  paid  in  the 
construction  of  dioptrical  instruments. 

23d  March,  1762, 

Hh2 


366  MEANS    OF    REMEDYING 


LETTER  CIIL 

Means  of  remedying  this  Defect  by  Compound  Object- 
glasses. 

IT  is  necessary  carefully  to  distinguish  this  new 
diffusion  or  multiplication  of  the  image,  arising  from 
the  different  refrangibility  of  rays,  as  being  of  differ- 
ent colours  from  the  first  diffusion,  occasioned  by 
the  aperture  of  the  lens,  inasmuch  as  the  rays  which 
pass  tnrough  the  extremities  form  another  image 
than  those  which  pass  through  its  middle.  This 
new  defect  must  accordingly  be  remedied  differently 
from  the  first. 

You  will  please  to  recollect  that  I  have  proposed 
two  methods  for  remedying  the  preceding  defect ; 
the  one  consisted  in  an  increase  of  the  focal  dis- 
tance, in  order  to  diminish  the  curve  of  the  surfaces 
of  the  lens.  This  remedy  introduces  instruments 
extremely  long  whenever  a  great  magnifying  power 
is  required.  The  other  consists  in  a  combination 
of  two  lenses,  the  one  convex  and  the  other  con- 
cave, to  modify  the  refraction,  so  that  all  the  rays 
transmitted  through  these  lenses  may  meet  in  the 
same  point,  and  the  space  of  diffusion  be  totally  re- 
duced. 

But  neither  of  these  remedies  affords  the  least  as- 
sistance towards  removing  the  inconvenience  arising 
from  the  different  refrangibility  of  rays.  The  first 
even  increases  the  evil ;  for  the  more  that  the  focal 
distance  is  increased,  the  more  considerable  becomes 
the  space  through  which  the  coloured  images  are 
dispersed.  Neither  does  the  combination  of  two  or 
more  lenses  furnish  any  assistance ;  for  we  are  as- 
sured, from  both  theory  and  experience,  that  the 
images  of  different  colours  remain  always  separated, 
however  great  the  number  of  lenses  through  which 


DEFECTS    IN    TELESCOPES.  367 

the  rays  are  transmitted,  and  that  the  more  the  lens 
magnifies,  the  more  the  difference  increases. 

This  difficulty  appeared  so  formidable  to  the  great 
Newton,  that  he  despaired  of  finding  a  remedy  for  a 
defect  which  he  believed  absolutely  inseparable  from 
dioptrical  instruments,  when  the  vision  is  produced 
by  refracted  rays.  For  this  reason  he  resolved  to 
give  up  refraction  altogether,  and  to  employ  mirrors 
instead  of  object-glasses,  as  reflection  is  always  the 
same  for  rays  of  every  nature.  This  idea  has  pro- 
cured for  us  those  excellent  reflecting  telescopes, 
whose  surprising  effects  are  so  justly  admired,  and 
which  I  shall  describe  after  I  have  explained  every 
thing  relative  to  refractive  instruments. 

On  being  convinced  that  it  was  impossible  to 
remedy  the  different  refrangibility  of  rays  by  a 
combination  of  several  lenses,  I  remarked  "that  the 
reason  of  it  was  founded  on  the  law  of  refraction, 
which  is  the  same  in  every  species  of  glasses  ;  and 
I  perceived  that  if  it  were  possible  to  employ  other 
transparent  substances,  whose  refraction  should  be 
considerably  different  from  that  of  glass,  it  might  be 
very  possible  to  combine  such  substance  with  glass, 
in  such  a  manner  that  all  the  rays  should  unite  in  the 
formation  of  a  single  image,  without  any  space  of 
diffusion.  In  pursuance  of  this  idea,  I  found  means 
to  compose  object-glasses  of  glass  and  water,  wholly 
exempt  from  the  effect  of  the  different  refrangibility 
of  rays,  which  consequently  would  produce  as  good 
an  effect  as  mirrors. 

I  executed  my  idea  with  two  menis-  Fig.  193. 
cuses,  or  concavo-convex  lenses,  Fig.  193, 
the  one  of  which  is  A  A  C  C,  and  the 
other  BBC  C,  which  I  joined  together 
with  the  concave  surfaces  towards  each 
other,  filling  the  void  between  them  with 
water,  so  that  the  rays  which  entered  by 
the  lens  A  A  C  C  must  pass  through  the  water  en- 
closed between  the  two  lenses,  before  they  went  off 


368  MEANS    OF    REMEDYING 

through  C  C  B  B.  Each  ray  undergoes,  then,  four 
refractions :  the  first  on  passing  from  the  air  into 
the  lens  A  A  C  C ;  the  second  on  passing  from  this 
lens  into  the  water ;  the  third  on  passing  thence  into 
the  other  lens  C  C  B  B ;  the  fourth  on  passing  from 
this  lens  into  the  air. 

As  the  four  surfaces  of  these  two  lenses  here  en- 
ter into  consideration,  I  found  means  to  determine 
their  semi-diameters,  so  that  of  whatever  colour  a 
ray  of  light  might  be,  after  having  undergone  these 
four  refractions,  it  should  reunite  in  the  same  point, 
and  the  different  refrangibility  no  longer  produce 
different  images. 

These  object-glasses,  compounded  of  two  lenses 
and  water,  were  found  subject  at  first  to  the  former 
defect,  namely,  that  of  the  rays  which  pass  through 
the  extremities  forming  a  different  focus  from  what 
is  formed  by  those  which  pass  through  the  middle ; 
but,  after  much  painful  research,  1  found  means  to 
proportion  the  radii  of  the  four  surfaces  in  such  a 
manner  that  these  comj 
wholb 
specif 

execute  so  exactly  all  the  measurements  prescribed 
by  the  calculation,  that  the  slightest  aberration  must 
become  fatal  to  the  whole  process  ;  I  was  therefore 
obliged  to  abandon  the  construction  of  these  object- 
glasses.* 

Besides,  this  project  could  remedy  only  the  incon- 
veniences which  affect  the  object-glass,  and  the  eye- 
glass might  still  labour  under  some  defect  as  great, 
which  it  would  be  impossible  to  remedy  in  the  same 
manner.  Several  eye-glasses  are  frequently  em- 
ployed in  the  construction  of  telescopes,  which  I 
shall  describe  afterward :  we  should  not,  therefore, 
gain  much  by  a  too  scrupulous  adherence  to  the  ob- 

*  Object-glasses  of  this  kind,  even  if  executed  in  the  most  correct 
manner,  are  incapable  of  producing  the  effects  which  our  author  expected 
from  them.— Ed. 


DEFECTS    IN    TELESCOPES.  369 

ject-glass  only,  while  we  overlook  the  other  lenses, 
though  their  effect  may  not  be  greatly  perceptible 
relatively  to  that  of  the  object-glass. 

But  whatever  pains  these  researches  may  have 
cost  me,  I  frankly  declare  that  I  entirely  give  up  at 
present  the  construction  of  object-glasses  com- 
pounded of  glasses  and  water ;  as  well  on  account 
of  the  difficulty  of  execution,  as  that  I  have  since 
discovered  other  means,  not  of  destroying  the  effect 
of  the  different  refrangibility  of  rays,  but  of  render- 
ing it  imperceptible.  This  shall  be  the  subject  of 
my  next  Letter. 

With  March,  1762. 


LETTER  CIV. 

Other  Means  more  practicable. 

SINCE  the  reflecting  telescope  came  into  general 
use,  refracting  ones  have  been  so  run  down  that  they 
are  on  the  point  of  being  wholly  laid  aside.  The 
construction  of  them  has  accordingly  for  some  time 
past  been  wholly  suspended,  under  a  firm  persuasion 
that  every  effort  to  raise  them  to  a  state  of  per- 
fection would  be  useless,  as  the  great  Newton  had 
demonstrated  that  the  insurmountable  difficulties 
arising  from  the  different  refrangibility  of  rays  was 
absolutely  inseparable  from  the  construction  of  tele- 
scopes. 

If  this  sentiment  be  well  founded,  there  is  no 
telescope  capable  of  representing  objects  but  with  a 
confusion  insupportable  in  proportion  to  the  great- 
ness of  the  magnifying  power.  However,  though 
there  are  telescopes  extremely  defective  in  this 
respect,  we  likewise  meet  with  some  that  are  excel- 
lent, and  nowise  inferior  to  the  so  much  boasted 
reflecting  telescopes.  This  is  undoubtedly  a  very 
great  paradox  ;  for  if  this  defect  really  attached  to 


370  MEANS    OF    REMEDYING 

the  subject,  we  should  not  find  a  single  exception. 
Such  an  exception,  therefore — and  we  have  the  testi- 
mony of  experience  that  it  exists — well  merits  every 
degree  of  attention. 

We  are  to  inquire,  then,  how  it  happens  that  cer- 
tain telescopes  represent  the  object  abundantly  dis- 
tinct, while  others  are  but  too  much  subject  to  the 
defect  occasioned  by  the  different  refrangibility  of 
rays.  I  think  I  have  discovered  the  reason,  which 
I  submit  in  the  following1  reflections  : — 

1.  It  is  indubitably  certain  that  the  object-glass 
represents  an  infinity  of  images  of  each  object, 
which  are  all  arranged  over  the  same  space  of  diffu- 
sion, and  each  of  which  is  painted  its  own  proper 
colour,  as  I  have  demonstrated  in  the  preceding 
Letter. 

2.  Each  of  these  images  becomes  an  object,  with 
respect  to  the  eye-glass,  which  represents  each  sep- 
arately, in  the  colour  proper  to  it ;  so  that  the  eye 
discovers,  through  the  telescope,  an  infinity  of  im- 
ages, disposed  in  a  certain  order,  according  to  the 
refraction  of  the  lens. 

3.  And  if,  instead  of  one  eye-glass,  we  were  to 
employ  several,  the  same  thing  will  always  take 
place,  and  instead  of  one  image,  the  telescope  will 
represent  an  infinity  to  the  eye,  or  a  series  of  im- 
ages, each  of  which  expresses  a  separate  object,  but 
of  a  particular  colour. 

4.  Let  us  now  consider,  Fig.  194,  the  last  images 


Fig.  194. 


presented  by  the  telescope  to  an  eye  placed  at  0, 
and  let  R  r  be  the  red  image,  and  V  v  the  violet,  those 
of  the  oth<>r  colours  being  between  these  two,  ac- 


DEFECTS    IN    TELESCOPES.  371 

cording  to  the  order  of  their  different  refrangibility. 
I  have  not  in  this  figure  introduced  the  lenses  of  the 
telescope,  the  only  point  at  present  being  to  show 
in  what  manner  the  eye  sees  the  images.  Only  we 
must  conceive  the  distance  of  the  eye  O  from  these 
images  to  be  very  great. 

5.  All  these  images  R  r  and  V  »,  with  the  inter- 
mediate, are  situated,  then,  on  the  axis  of  the  tele- 
scope O  R  V,  and  terminated  by  a  certain  straight 
line,  r  v,  denominated  the  terminatrix  of  all  the 
images. 

6.  As  I  have  represented  these  images  in  the 
figure,  the  red  image  R  r  is  seen  by  the  eye  at  O, 
under  the  angle  R  O  r,  which  is  greater  than  the 
angle  V  O  v,  under  which  the  violet  image  V  v  is 
seen.     The  violet  rays  which,  from  the  image  V  v, 
enter  into  the  eye,  are  therefore  blended  with  the 
red  which  come  from  the  part  R  r  of  the  red  image 
Rr. 

7.  Consequently,  the  eye  cannot  see  the  violet 
image  without  a  mixture  of  rays  of  other  colours, 
but  which  correspond  to  different  points  of  the  ob- 
ject itself;  thus  the  point  n  of  the  red  image  is 
confounded  in  the  eye  with  the  extremity  v  of  the 
violet  image,  from  which  a  very  great  confusion 
must  arise. 

8.  But  the  ray  r  O  not  being  mix'ed  with  the 
others,  the  extremity  seen  will  appear  red,  or  the 
image  will  seem  bordered  With  red,  which  afterward 
successively  blends  with  these  other  colours,  so  that 
the  object  will  appear  with  a  party-coloured  border; 
a  fault  very  common  in  telescopes,  to  which  some, 
however,  are  less  subject  than  others. 

9.  If  the  greater  image  R  r  were  the  violet,  and 
V  v  the  red,  the  confusion  would  be  equally  offen- 
sive, with  this  difference  only,  that  the  extremities 
of  the  object  would  then  appear  bordered  with  vio- 
let instead  of  red. 

10.  The  confusion  depends,  then,  on  the  position 


372      OF  REMEDYING  DEFECTS  IN  TELESCOPES. 

of  the  terminating  straight  line  r  v  with  relation  to 
the  line  V  O,  and  the  diversity  which  may  take 
place  in  it ;  the  result  must  be,  that  the  confusion 
will  be  sometimes  greater  and  sometimes  less. 

11.  Let  us  now  consider  the  case  in  which  the 
last  images  represented  by  the  telescope  are  so 
arranged,  that  the  straight  terminating  line  v  r,  being 
produced,  would  pass  precisely  into  the  eye.  The 
eye  will  then  see,  Fig.  195,  along  a  single  ray  v  r  O, 


Fig.  195. 


all  the  extremities ;  and,  in  general,  all  the  points 
which  correspond  to  one  and  the  same  point  of  the 
object  will  be  conveyed  to  the  eye  by  a  single  ray, 
and  will  there,  consequently,  be  distinctly  repre- 
sented. 

12.  Here,  then,  is  a  case  in  which,  notwithstand- 
ing the  diversity  of  images,  the  eye  may  see  the 
object  distinctly,  without  any  confusion  of  the  dif- 
ferent parts,  as  happened  hi  the  preceding  case. 
This  advantage,  then,  will  be  obtained  when  the  ter- 
minating line  v  r,  being  produced,  passes  through 
the  place  of  the  eye  O. 

13.  As  the  arrangement  of  the  last  images  R  r 
and  V  v  depends  on  the  disposition  of  the  eye-glasses, 
in  order  to  rescue  telescopes  from  the  defect  im- 
puted to   them,  nothing  more   is  requisite  but  to 
arrange  these  lenses  in  such  a  manner  that  the  ter- 
minating line   of  the  last   images  v  r  shall  pass 
through  the  eye;  and  telescopes  thus  constructed 
will  always  be  excellent. 

30th  March,  1762. 


QUALITIES    OF   A   GOOD   TELESCOPE.          373 


LETTER  CV. 

Recapitulation  of  the  Qualities  of  a  good  Telescope. 

ON  taking  a  general  review  of  the  subject,  you 
will  readily  admit  that  an  excellent  telescope  is  a 
most  valuable  commodity,  but  rarely  to  be  met  with, 
being  subject  to  so  many  defects,  and  so  many  quali- 
ties being  requisite,  each  of  which  has  an  essential 
influence  on  the  construction  of  the  instrument. 
As  the  number  of  the  good  qualities  is  considerable, 
in  order  that  no  one  of  them  may  escape  your  ob- 
servation, I  shall  again  go  over  the  ground,  and 
make  a  distinct  enumeration  of  them. 

1.  The  first  respects  the  magnifying  power  ;  and 
the  more  that  a  telescope  magnifies  objects,  the 
more  perfect  undoubtedly  it  is,  provided  that  no 
other  good  quality  is  wanting.     Now,  the  magnify- 
ing power  is  to  be  estimated  from  the  number  of 
times  that  the  diameter  of  the  object  appears  greater 
than  to  the  naked  eye.     You  will  recollect  that,  in 
telescopes  of  two  lenses,  the  magnifying  power  is 
so  many  times  greater  as  the  focal  distance  of  the 
object-glass  exceeds  that  of  the  eye-glass.     In  tele- 
scopes consisting  of  more  lenses  than  two,  the 
determination  of  the  magnifying  power  is  more  in- 
tricate. 

2.  The  second  property  of  a  good  telescope  is 
brightness.     It  is  always  very  defective  when  it  rep- 
resents the  object  obscurely,  and  as  through  a  mist. 
In  order  to  avoid  this  defect,  the  object-glass  must 
be  of  such  a  size  as  is  regulated  by  the  magnifying 
power.     Artists  have  determined  that,  in  order  to 
magnify  300  times,  the  aperture  of  the  object-glass 
ought  to  be  three  inches  diameter ;  and  for  every 
other  magnifying  power  in  proportion.     And  when 
objects  are   not  very  luminous  of  themselves,  it 

VOL.  II.— I  i 


374  QUALITIES    OF   A 

would  be  proper  to  employ  object-glasses  of  a  still 
greater  diameter. 

3.  The  third  quality  is  distinctness  or  accuracy 
of  representation.     In  order  to  produce  this,  the  rays 
which  pass  through  the  extremities  of  the  object- 
glass  ought  to  meet  in  the  same  point  with  those 
which  pass  through  the  middle,  or  at  least  the  aber- 
ration should  not  be  perceptible.     When  a  simple 
object-glass  is  employed,  its  focal  distance  must 
exceed  a  certain  limit  proportional  to  the  magnify- 
ing power.     Thus,  if  you  wish  to  magnify  100  times, 
the  focal  distance  of  the  object-glass  must  be  at 
'east  30  feet.     It  is  the  destination,  therefore,  which 
imposes  the  necessity  of  making  telescopes  so  ex- 
cessively long,  if  we  want  to  obtain  a  very  great 
magnifying  power.     Now,  in  order  to  remedy  this 
defect,  an  object-glass  composed  of  two  lenses  may 
be  employed ;  and  could  artists  succeed  in  the  con- 
struction of  them,  we  should  be  enabled  very  con- 
siderably to  shorten  telescopes,  while  the   same 
magnifying1  power  remained.     You  will  have  the 
goodness  to  recollect  what  I  have  already  suggested 
at  some  length  on  this  subject. 

4.  The  fourth  quality  regards  likewise  the  dis- 
tinctness or  purity  of  representation,  as  far  as  it  is 
affected  by  the  different  refrangibility  of  rays  t)f 
different  colours.     I  have  shown  how  that  defect 
may  be  remedied ;  and  as  it  is  impossible  that  the 
images  formed  by  different  rays  should  be  collected 
in  a  single  one,  the  point  in  question  is  to  arrange 
the  lenses  in  the  manner  I  have  described  in  the 
preceding  Letter ;  that  is,  the  terminating  line  of  the 
last  images  must  pass  through  the  eye.     Without 
this,  the  telescope  will  have  the  defect  of  repre- 
senting objects  surrounded  with  the  colours  of  the 
rainbow  ;  but  the  defect  will  disappear  on  arranging 
the  lenses  in  the  method  I  have  pointed  out.     But 
to  this  effect,  more  than  two  lenses  must  be  em- 
ployed, in  order  to  a  proper  arrangement.    I  have 


GOOD    TELESCOPE.  375 

hitherto  spoken  only  of  telescopes  with  two  lenses, 
one  of  which  is  the  object-glass,  and  the  other  the 
eye-glass ;  and  you  know  that  their  distance  from 
each  other  is  already  determined  by  their  focal  dis- 
tances, so  that  here  we  are  not  at  liberty  to  make 
any  alteration.  It  happens,  fortunately,  however, 
that  the  terminating  line  which  I  have  mentioned 
passes  nearly  through  the  place  of  the  eye,  so  that 
the  defect  arising  from  the  colours  of  the  rainbow 
is  almost  imperceptible,  provided  the  preceding  de- 
fect is  remedied,  especially  when  the  magnifying 
power  is  not  very  great.  But  when  the  power  is 
considerable,  it  would  be  f -roper  to  employ  two  eye- 
glasses, in  order  entirely  to  annihilate  the  colours 
of  the  rainbow,  as  in  this  case  the  slightest  defects, 
being  equally  magnified,  become  insupportable. 

5.  The  fifth  and  last  good  quality  of  a  telescope 
is  a  large  apparent  field,  or  the  space  which  the  in- 
strument discovers  at  once.  You  recollect  that 
small  pocket-glasses  with  a  concave  eye-glass  are 
subject  to  the  defect  of  presenting  a  very  small 
field,  which  renders  them  incapable  of  magnifying 
greatly.  The  other  species,  that  with  a  convex 
eye-glass,  is  less  subject  to  this  defect ;  but  as  it 
represents  the  object  inverted,  telescopes  of  the  first 
species  would  be  preferable,  did  they  discover  a 
larger  field,  which  depends  on  the  diame'ter  of  the 
aperture  of  the  eye-glass ;  and  you  know  we  can- 
not increase  this  aperture  at  pleasure,  because  it  is 
determined  by  focal  distance.  But  by  employing 
two  or  three,  or  even  more  eye-glasses,  we  have 
found  means  to  render  the  apparent  field  greater ; 
and  this  is  an  additional  reason  for  employing  seve- 
ral lenses  in  order  to  procure  a  telescope  in  all  re- 
spects excellent. 

To  these  good  qualities  another  may  be  still  added, 
that  the  representation  shall  not  be  inverted  by  the 
instrument,  as  by  astronomical  telescopes.  But  this 
defect  may  be  easily  remedied,  if  it  be  one,  by  the 


376        TERRESTRIAL  TELESCOPES 

addition  of  two  more  eye-glasses,  as  I  shall  show 
in  my  next  Letter. 
3d  April,  1762. 


LETTER  CVI. 

Terrestrial  Telescopes  with  four  Lenses. 

I  HAVE  treated  at  considerable  length  of  telescopes 
composed  of  two  convex  lenses,  known  by  the  name 
of  astronomical  tubes,  because  they  are  commonly 
used  for  observing  the  heavenly  bodies. 

You  will  readily  comprehend  that  the  use  of  such 
instruments,  however  excellent  they  may  be,  is 
limited  to  the  heavens,  because  they  represent  ob- 
jects in  an  inverted  position,  which  is  very  awkward 
in  contemplating  terrestrial  bodies,  as  we  would 
rather  wish  to  view  them  in  their  natural  situation; 
but  on  the  discovery  of  this  species  of  telescope, 
means  were  quickly  found  of  remedying  that  defect, 
by  doubling,  if  I  may  say  so,  the  same  telescope. 
For  as  two  lenses  invert  the  object,  or  represent  the 
image  inverted,  by  joining  a  similar  telescope  to  the 
former,  for  viewing  the  same  image,  it  is  again  in- 
verted, and  this  second  representation  will  exhibit 
the  objecc  upright.  Hence  arose  a  new  species  of 
telescopes,  composed  of  four  lenses,  called  terres- 
trial telescopes,  from  their  being  designed  to  con- 
template terrestrial  objects ;  and  the  method  of 
constructing  them  follows. 

1.  The  four  lenses  A,  B,  C,  D,  Fig.  189,  enclosed 
Fig.  189. 


WITH    FOUR    LENSES.  377 

in  the  tube  M  M  N  N,  represent  the  telescope  in 
question ;  the  first  of  which,  A,  directed  towards  the 
object,  is  denominated  the  object-glass,  and  the  other 
three,  BCD,  the  eye-glass.  These  four  lenses 
are  all  convex,  and  the  eye  must  be  placed  at  the 
extremity  of  the  tube,  at  a  certain  distance  from  the 
last  eye-glass  D,  the  determination  of  which  shall 
be  afterward  explained. 

2.  Let  us  consider  the   effect  which  each  lens 
must  produce  when  the  object  O  0, which  is  viewed 
through  the  telescope,  is  at  a  very  great  distance. 
The  object-glass  will  first  represent  the  image  of 
this  object  at  P  p,  its  focal  distance,  the  magnitude 
of  the  image  being  determined  by  the  straight  line 
drawn  from  the  extremity  o  through  the  centre  of 
the  lens  A.     This  line  is  not  represented  in  the 
figure,  that  it  may  not  be  embarrassed  with  too  many 
lines. 

3.  This  image  P  p  occupies  the  place  of  the  ob- 
ject with  respect  to  the  second  lens  B,  which  is 
placed  in  such  a  manner  that  the  interval  B  P  shall 
be  equal  to   its  focal  distance,  in  order  that  the 
second  image  may  be  thence  transported  to  an  infi- 
nite distance,  as  Q  q,  which  will  be  inverted  as  the 
first  P  p,  and  terminated  by  the  straight  line  drawn 
from  the  centre  of  the  lens   B  through  the  ex- 
tremity p, 

4.  The  interval  between  these  two  first  lenses 

A,  B  is  equal,  therefore,  to  the  sum  of  their  focal 
distances ;  and  were  the  eye  placed  behind  the  lens 

B,  we  should  have  an  astronomical  telescope,  through 
which  the  object  O  o  would  be  seen  at  Q  q,  and 
consequently  inverted,  and  magnified  as  many  times 
as  the  distance  A  P  exceeds  the  distance  B  P.     But 
instead  of  the  eye,  we  place  behind  the  lens  B,  at 
some  distance,  the  third  lens  C,  with  respect  to 
which  the  image  Q  q  occupies  the  place  of  the  ob- 
ject, as  in  fact  it  receives  the  rays  from  this  image 
Q  q,  which  being  at  a  very  great  distance,  the  lens 

I  i  2 


378        TERRESTRIAL  TELESCOPES. 

C  will  represent  the  image  of  it,  at  its  focal  distance, 
in  Rr. 

5.  The  image  Q  q  being  inverted,  the  image  R  r 
will  be  upright,  and  terminated  by  the  straight  line 
drawn  from  the  extremity  q  through  the  centre  of 
the  lens  C,  which  will  pass  through  the  point  r. 
Consequently  the  three  lenses  A,  B,  C  together  rep- 
resent the  object  O  o  at  R  r,  and  this  image  R  r  is 
upright. 

0.  Finally,  we  have  only  to  place  the  last  lens  in 
such  a  manner  that  the  interval  D  R  shall  be  equal 
to  its  focal  distance ;  this  lens  D  will  again  trans- 
port the  image  R  r  to  an  infinite  distance,  as  S  s, 
the  extremity  of  which  s  will  be  determined  by  the 
straight  line  drawn  from  the  centre  of  the  lens  D 
through  the  extremity  r ;  and  the  eye  placed  behind 
this  lens  will  in  fact  see  this  image  S  s  instead  of  the 
real  object  O  o. 

7.  Hence  it  is  easy  to  ascertain  how  many  times 
this  telescope,  composed  of  four  lenses,  must  mag- 
nify the  object ;  you  have  only  to  attend  to  the  two 
couple  of  lenses,  A,  B  and  C,  D,  each  of  which 
separately   would   be  an   astronomical   telescope. 
The  first  pair  of  lenses  A  and  B  magnifies  as  many 
times  as  the  focal  distance  of  the  first  lens  A  ex- 
ceeds that  of  the  second  lens  B  ;  and  so  many  times 
will  the  image  formed  by  it,  Q  q,  exceed  the  real 
object  O  o. 

8.  Further,  this  image  Q  q  occupying  the  place 
of  the  object  with  respect  to  the  other  pair  of  lenses 
C  and  D,  it  will  be  again  multiplied  as  many  times 
as  the  focal  distance  of  the  lens  C  exceeds  that  of 
the  lens  D.     These  two  magnifying  powers  added 
give  the  whole  magnifying  power  produced  by  the 
four  lenses. 

9.  If,  then,  the  first  pair  of  lenses,  A  and  B,  mag- 
nify ten  times,  and  the  other  pair,  C  and  D,  three 
times,  the  telescope  will  magnify  the  object  thrice 
ten,  that  is,  thirty  times ;  and  the  aperture  of  the 


ARRANGEMENT    OF    LENSES.  379 

object-glass  A  must  correspond  to  this  magnifying 
power,  according  to  the  rule  formerly  laid  down. 

10.  Hence  you  see,  then,  that  on  separating  from 
a  terrestrial  telescope  the  two  last  lenses  C  and  D, 
there  would  remain  an  astronomical  telescope,  and 
that  these  two  lenses  C  and  D  would  likewise  form 
sucn  a  telescope.  A  terrestrial  telescope,  therefore, 
consists  of  two  astronomical  ones ;  and  reciprocally, 
two  astronomical  telescopes  combined  form  a  ter- 
restrial one. 

This  construction  is  susceptible  of  endless  varia- 
tions, some  preferable  to  others,  as  I  shall  afterward 
demonstrate. 

Qth  April,  1762. 


LETTER  CVII. 

Arrangement  of  Lenses  in  Terrestrial  Telescopes. 

You  have  seen  how,  by  the  addition  of  two  con- 
vex lenses  to  an  astronomical  telescope,  a  terres- 
trial one  is  produced,  which  represents  the  object 
upright.  The  four  lenses  of  which  a  terrestrial  tele- 
scope is  composed  are  susceptible  of  an  infinite 
variety  of  arrangement,  with  respect  to  both  focus 
and  distance.  I  shall  explain  those  which  are  of 
most  essential  importance,  and  refer  you  to  Fig.  196. 

Fig.  196. 
a, 

T> 


1.  With  respect  to  their  distances,  I  have  already 
remarked  that  the  interval  between  the  two  first 
lenses,  A  and  B,  is  the  sum  of  their  focal  distances ; 
and  the  same  thing  holds  as  to  the  last  lenses  C  and 


380  ARRANGEMENT    OF    LENSES 

D :  for  each  pair  may  be  considered  as  a  simple 
telescope,  composed  of  two  convex  lenses.  But 
what  must  be  the  interval  between  the  two  middle 
lenses  B  and  C  1  May  it  be  fixed  at  pleasure  1  As 
it  is  certain  that  whether  this  interval  be  great  or 
small,  the  magnifying-  power,  always  compounded 
of  the  two  which  each  pair  would  produce  separafely, 
must  continue  the  same. 

2.  On  consulting  experience  we  soon  perceive 
that  when  the  two  middle  lenses  are  placed  very  near 
each  other,  the  apparent  field  almost  entirely  van- 
ishes ;  and  the  same  thing  takes  place  when  they  are 
too  far  separated.     In  both  cases,  to  whatever  object 
the  telescope  is  pointed,  we  discover  only  a  very 
small  part  of  it. 

3.  For  this  reason  artists  bring  the  last  pair  of 
lenses  nearer  to  the  first,  or  remove  them  to  a 
greater  distance,  till  they  discover  the  largest  field, 
and  delay  fixing  the  lenses  till  they  have  found  this 
situation.     Now  they  have  observed,  that  in  settling 
this  most  advantageous  arrangement,  the  distance 
of  the  middle  lenses,  B  and  C,  is  always  greater 
than  the  sum  of  the  focal  distances  of  these  same 
two  lenses. 

4.  You  will  readily  conclude  that  this  distance 
cannot  depend  on  chance,  but  must  be  supported  by 
a  theory,  and  that  affording  a  termination  much  more 
exact  than  what  experience  alone  could  have  fur- 
nished.    As  it  is  the  duty  of  a  natural  philosopher 
to  investigate  the  causes  of  all  the  phenomena  which 
experience  discovers,  I  proceed  to  unfold  the  true 
principles  which  determine  the  most  advantageous 
distance  B  C  between  the  two  middle  lenses.     For 
this  purpose  I  refer  to  Fig.  197. 

Fig.  197. 


IN  TERRESTRIAL  TELESCOPES.       381 

5.  As  all  the  rays  must  be  conveyed  to  the  eyer/ 
let  us  attend  to  the  direction  of  that  one  which,  pro- 
ceeding from  the  extremity  O  of  the  visible  object, 
passes  through  the  centre  A  of  the  object-glass  ;  for 
unless  this  ray  is  conveyed  to  the  eye,  this  extremity 
O  will  not  be  visible.     Now  this  ray  undergoes  no 
refraction  in  the  object-glass,  for  it  passes  through 
the  centre  A  ;  it  will  therefore  proceed  in  a  straight 
line  to  the  second  lens,  which  it  will  meet  in  its  ex- 
tremity b,  as  this  is  the  last  ray  transmitted  through 
the  lenses. 

6.  This  ray,  being  refracted  by  the  second  lens, 
will  change  its  direction  so  as  to  meet  somewhere 
at  n  the  axis  of  the  lenses ;  this  would  have  hap- 
pened to  be  the  focus  of  this  lens,  had  the  ray  A  b 
been  parallel  to  the  axis  ;  but  as  it  proceeds  from 
the  point  A,  its  reunion  with  the  axis  at  n  will  be 
more  distant  from  the  lens  B  than  its  focal  distance. 

7.  We  must  now  place  the  third  lens  C  in  such  a 
manner  that  the  ray,  after  having  crossed  the  axis 
at  n,  may  meet  it  exactly  in  its  extremity  c  ;  from 
which  it  is  evident,  that  the  greater  the  aperture  of 
this  lens  C  is,  the  farther  it  must  be  removed  from 
the  lens  B,  and  the  greater  the  interval  B  C  becomes : 
but,  on  the  other  hand,  care  must  be  taken  not  to 
remove  the  lens  C  beyond  that  point,  as  in  this  case 
the  ray  would  escape  it,  and  be  transmitted  no  far- 
ther.   This  circumstance,  then,  determines  the  just 
distance  between  the  two  middle  lenses  B  and  C, 
conformably  to  experience. 

8.  This  lens  C  will  produce  a  new  refraction  of 
the  ray  in  question,  which  will  convey  it  precisely 
to  the  extremity  d  of  the  last  eye-glass  D,  which, 
being  smaller  than  C,  will  render  the  line  c  d  some- 
what convergent  towards  the  axis,  and  will  thus 
undergo,  in  the  last  lens,  such  a  degree  of  refraction 
as  will  reunite  it  with  the  axis  at  less  than  its  focal 
distance ;  and  there  it  is  exactly  that  the  eye  must 
be  placed,  in  order  to  receive  all  the  rays  trans- 


382  CONSTRUCTION   OF   TELESCOPES. 

mitted  through  the   lenses,  and  to  discover  the 
greatest  field. 

9.  Thus  we  are  enabled  to  procure  a  field  whose 
diameter  is  almost  twice  as  large  as  with  an  astro- 
nomical telescope  of  the  same  magnifying  power. 
By  means,  then,  of  these  telescopes  with  four  lenses 
we  obtain  a  double  advantage  ;  the  object  is  repre- 
sented upright,  and  a  much  larger  field  is  discovered 
— both  circumstances  of  much  importance. 

10.  Finally,  it  is  possible  to  find  such  an  arrange- 
ment of  these  four  lenses  as,  without  affecting  either 
of  the  advantages  now  mentioned,  shall  entirely  do 
away  the  defect  arising  from  the  colours  of  the  rain- 
bow, and  at  the  same  time  represent  the  object  with 
all  possible  distinctness.     But  few  artists  can  attain 
this  degree  of  perfection. 

Wth  April,  1762. 


LETTER  CVIII. 

i  of 

scopes.     Necessity  of  blackening  the  Inside  of  Tubes. 
Diaphragms. 

AFTER  these  researches  respecting  the  construc- 
tion of  telescopes,  I  must  suggest  and  explain  certain 
precautions  necessary  to  be  used;  which,  though 
they  relate  neither  to  the  lenses  themselves  nor  to 
their  arrangement,  are  nevertheless  of  such  import- 
ance, that  if  they  are  not  very  carefully  observed, 
the  best  instrument  is  rendered  entirely  useless.  It 
is  not  sufficient  that  the  lenses  should  be  arranged 
in  such  a  manner  that  all  the  rays  which  fall  upon 
them  shall  be  transmitted  through  these  lenses  to 
the  eye  ;  care  must  be  taken,  besides,  to  prevent  the 
transmission  of  extraneous  rays  through  the  tele- 
scope to  disturb  the  representation.  Let  the  fol- 
lowing precautions,  then,  be  taken. 


CONSTRUCTION  OF  TELESCOPES.      383 

1.  The  lenses  of  which  a  telescope  is  composed 
must  be  enclosed  in  a  tube,  that  no  other  rays  ex- 
cept those  which  are  transmitted  through  the  object- 
glass  may  reach  the  other  lenses.     For  this  effect, 
the  tube  must  be  so  very  close  throughout  that  no 
chink  admits  the  smallest  portion  of  light.     If  by  any 
accident  the  tube  shall  be  perforated  ever  so  slightly, 
the  extraneous  light  admitted  would  confound  the 
representation  of  the  object. 

2.  It  is  likewise  of  importance  to  blacken  through- 
out the  inside  of  the  telescope,  of  the  deepest  black 
possible,  as  it  is  well  known  that  this  colour  does 
not  reflect  the  rays  of  light,  be  they  ever  so  power- 
ful.    You  must  have  observed,  accordingly,  that  the 
tubes  of  telescopes  are  always  blackened  internally. 
A  single  reflection  will  show  the  necessity  of  it. 

3.  The  object-glass  A,  Fig.  199,  trans- 
mits, not  only  the  rays  of  the  object  rep-    Fig.  199. 
resented  by  the  telescope,  but  those  also        \p 
which  by  the  extremities  enter  all  around 

in  great  abundance  ;  such  is  the  ray  b  a, 
which  falls  on  the  inside  upon  the  frame 
of  the  tube  at  i :  if,  therefore,  the  tube 
were  white  inwardly,  or  of  any  other 
colour,  it  would  be  illuminated  by  this 
ray,  and  of  itself  would  generate  new 
rays  of  light,  which  must  of  necessity  be 
conveyed  through  the  other  lenses,  and 
disturb  the  representation,  by  mingling 
with  the  proper  rays  of  the  object. 

4.  But  if  the   inside  of  the  tube  be 
blackened  deeply,  no  new  rays  will  be 
produced,  let  the  light  be  ever  so  strong.      This 
blackening  must  be  carried  through  the  whole  length 
of  the  telescope,  as  there  is  no  black  so  deep  as  not 
to  generate,  when  illuminated,  some  faint  light. 
Supposing,  then,  that  some  extraneous  rays  were 
to  make  their  way  to  the  second  lens  B,  the  black 
of  the  tube,  pursuing  their  course,  would  easily 


384  CONSTRUCTION   OF    TELESCOPES. 

absorb  them  altogether.  There  is  a  brilliant  black, 
which,  for  this  reason,  it  would  be  very  improper  to 
employ. 

5.  But  even  this  precaution  is  not  sufficient,  it  is 
necessary  likewise  to  furnish  the  inside  of  the  tube 
with  one  or  more  diaphragms,  perforated  with  a  small 
circular  aperture,  the  better  to  exclude  all  extraneous 
light ;  but  care  must  be  taken  that  they  do  not  ex- 
clude the  rays  of  the  object  which  the  instrument  is 
intended  to  represent.     See  Fig.  198. 

6.  It  is  necessary  to  observe  at  what   Fig.  198. 
place  in  the  tube  the  proper  rays  of  the  A 
object  are  most  contracted ;  this  must  be 

at  the  points  where  their  images  are 
represented,  for  there  all  the  rays  are 
collected  together.  Now,  the  object- 
glass  A  represents  the  image  in  its  focus 
at  M.  You  have  only,  then,  to  compute 
the  magnitude  of  this  image,  and  there 
to  fix  your  diaphragm,  whose  aperture 
m  n  shall  be  equal  to  the  magnitude  of  the 
image,  or  rather  somewhat  greater.  For 
if  the  aperture  were  less  than  the  image, 
there  would  be  a  proportional  loss  of  the 
apparent  field,  which  is  always  a  great 
defect. 

7.  These  are  the  observations  respecting  the  dia- 
phragm which   apply  to   astronomical   telescopes 
composed  of  two  convex  lenses.     In  terrestrial  tele- 
scopes two  images  are  represented  within  the  tube  ; 
besides  the  first  at  M,  represented  by  the  object- 
glass  in  its  focus,  and  which  the  second  lens  B  trans- 
ports to  an  infinite  distance,  the  third  lens  represents 
a  second  image  in  its  focus  N,  which  is  upright, 
whereas  the  former  was  inverted.     At  N,  therefore, 
is  the  proper  place  to  fix  a  second  diaphragm  perfo- 
rated with  an  aperture  n  n,  of  the  magnitude  of  the 
image  there  represented. 

8.  These  diaphragms,  aided  by  the  blackness  of 


OF    TELESCOPES.  385 

the  inside  of  the  tube,  produce  likewise  an  excellent 
effect  with  respect  to  distinctness  of  representation. 
It  must  be  carefully  observed,  however,  that  the 
greater  the  field  is  which  the  telescope  discovers, 
the  less  is  to  be  expected  from  these  diaphragms,  as 
in  that  case  the  images  become  greater,  so  that  the 
aperture  of  the  diaphragms  must  be  so  enlarged  as 
to  render  them  incapable  of  any  longer  excluding  the 
extraneous  rays.  So  much  the  greater  care,  there- 
fore, must  be  taken  thoroughly  to  blacken  the  inside 
of  the  tube,  and  to  make  it  larger,  which  consider- 
ably diminishes  the  unpleasant  effect  of  which  I  have 
been  speaking. 
13th  April,  1762. 


LETTER  CIX. 

In  what  manner  Telescopes  represent  the  Moon,  the 
Planets,  the  Sun,  and  the  Fixed  Stars.  Why  these 
last  appear  smaller  through  the  Telescope  than  to  the 
naked  Eye.  Calculation  of  the  Distance  of  the  Fixed 
Stars,  from  a  Comparison  of  their  apparent  Magni- 
tude with  that  of  the  Sun. 

I  AM  persuaded,  that  by  this  time  you  are  very 
well  pleased  to  be  relieved  at  length  from  the  dry 
theory  of  telescopes,  which  is  rendered  agreeable 
only  by  the  importance  of  the  discoveries  which 
they  have  enabled  us  to  make. 

What  pleasing  surprise  is  felt  on  seeing  very  dis- 
tant objects  as  distinctly  as  if  they  were  one  hundred 
times  nearer  to  us,  or  more  especially  in  cases  where 
there  is  no  possibility  of  reaching  them,  which  holds 
with  respect  to  the  heavenly  bodies  !  And  you  are 
already  disposed  to  admit,  that  with  the  aid  of  the 
telescope  many  wonderful  things  relating  to  the  stars 
have  been  discovered. 

On  viewing  the  moon  one  hundred  times  nearer 

VOL.  II.— K  k 


386  OF    TELESCOPES. 

than  she  really  is,  many  curious  inequalities  are  dis- 
cernible ;  such  as  excessive  heights  and  profound 
depths,  which  from  their  regularity  resemble  rather 
works  of  art  than  natural  mountains.  Hence  a 
very  plausible  argument  is  deduced  to  prove  that 
the  moon  is  inhabited  by  reasonable  creatures.  But 
we  have  proofs  still  more  satisfactory  in  simply 
contemplating  the  almighty  power,  in  union  with 
the  sovereign  wisdom  and  goodness  of  the  Great 
Creator. 

Thus  the  most  important  discoveries  have  been 
made  respecting  the  planets,  which,  to  the  unassisted 
eye,  appear  only  as  so  many  luminous  points ;  but 
which,  viewed  through  a  good  telescope,  resemble 
the  moon,  and  appear  even  still  much  greater. 

But  you  will  be  not  a  little  surprised,  when  I 
assure  you  that  with  the  assistance  of  the  best  tele- 
scope, even  one  which  magnifies  more  than  two 
hundred  times,  the  fixed  stars  still  appear  only  as 
points,  nay,  still  smaller  than  to  the  naked  eye.  This 
is  so  much  the  more  astonishing,  that  it  is  certain 
the  telescope  represents  them  such  as  they  would 
appear  were  we  two  hundred  times  nearer.  Are  we 
not  hence  reduced  to  the  necessity  of  concluding, 
that  here  telescopes  fail  to  produce  their  effect"? 
But  this  idea  presently  vanishes,  on  considering  that 
they  discover  to  us  millions  of  little  stars  which, 
without  their  aid,  must  have  for  ever  escaped  the 
eye.  We  likewise  perceive  the  distances  between 
the  stars  incomparably  greater ;  for  two  stars  which 
to  the  naked  eye  seemed  almost  to  touch  each  other, 
when  viewed  through  the  telescope  are  seen  at  a 
very  considerable  distance  ;  a  sufficient  proof  of  the 
effect  of  the  telescope. 

What,  then,  is  the  reason  that  the  fixed  stars  ap- 
pear to  us  smaller  through  the  telescope  than  to  the 
naked  eye  1  In  resolving  this  question,  I  remark, 
first,  that  the  fixed  stars  appear  greater  to  the  naked 
eye  than  they  ought  to  do,  and  that  this  arises  from 


OF    TELESCOPES.  387 

a  false  light  occasioned  by  their  twinkling1.  In  fact, 
when  the  rays  proceeding  from  a  star  come  to  paint 
their  image  at  the  bottom  of  the  eye,  on  the  retina, 
our  nerves  are  struck  by  it  only  in  one  point ;  but 
by  the  lustre  of  the  light  the  adjacent  nerves  likewise 
undergo  a  concussion,  and  produce  the  same  feeling 
which  would  be  communicated  if  the  image  of  the 
object  painted  on  the  retina  were  much  greater. 
This  happens  on  looking,  in  the  night,  at  a  very 
distant  light.  It  appears  much  greater  than  when 
we  view  it  at  a  small  distance  ;  and  this  increase  of 
magnitude  is  occasioned  only  by  a  false  glare.  Now, 
the  more  that  a  telescope  magnifies,  the  more  this 
accident  must  diminish ;  not  only  because  the  rays 
are  thereby  rendered  somewhat  fainter,  but  because 
the  real  image  at  the  bottom  of  the  eye  becomes 
greater ;  so  that  it  is  no  longer  a  single  point  which 
supports  the  whole  impression  of  the  rays.  Accord- 
ingly, however  small  the  stars  may  appear  through 
a  telescope,  we  may  confidently  affirm,  that  to  the 
naked  eye  they  would  appear  still  much  smaller  but 
for  this  accidental  false  light,  and  that  as  many  times 
as  the  telescope  magnifies. 

Hence  it  follows,  that  as  the  fixed  stars  appear 
only  like  so  many  points,  though  magnified  more 
than  200  times,  their  distance  must  be  inconceivable. 
It  will  be  easy  for  you  to  form  a  judgment  how  this 
distance  may  be  computed.  The  diameter  of  the 
sun  appears  under  an  angle  of  32  minutes :  if,  there- 
fore, the  sun  were  32  times  farther  off,  he  would 
appear  under  an  angle  of  one  minute  ;  and,  conse- 
quently, still  much  greater  than  a  fixed  star  viewed 
through  the  telescope,  the  diameter  of  which  does 
not  exceed  two  seconds,  or  the  thirtieth  part  of  a 
minute.  The  sun,  therefore,  must  be  thirty  times 
more,  that  is  960  times,  farther  removed,  before  his 
appearance  could  be  reduced  to  that  of  a  fixed  star 
observed  with  the  assistance  of  a  telescope.  But 
the  fixed  star  is  200  times  farther  off  than  the  tele- 


APPARENT  MAGNITUDE  OF  THE 

scope  represents  it ;  and,  consequently,  the  sun  must 
be  200  times  960,  that  is,  192,000  times  farther  off 
than  he  is,  before  he  could  be  reduced  to  the  appear- 
ance of  a  fixed  star.  It  follows,  that  if  the  fixed 
stars  were  bodies  as  large  as  the  sun,  their  distances 
would  be  192,000  times  greater  than  that  of  the  sun. 
Were  they  still  greater,  their  distances  must  be  still 
so  many  times  greater;  and  supposing  them  even 
many  times  smaller,  their  distances  must  always  be 
more  than  a  thousand  times  greater  than  that  of  the 
sun.  Now  the  distance  of  the  sun  from  our  globe  is 
about  96,000,000  of  English  miles. 

It  is  impossible,  undoubtedly,  to  think  of  this  im- 
mense distance  of  the  fixed  stars,  and  of  the  extent 
of  the  whole-  universe,  without  astonishment.  What 
must  be  the  power  of  that  Great  Being  who  created 
this  vast  fabric,  and  who  is  the  absolute  Master  of 
it  ]  Let  us  adore  Him  with  the  most  profound  ven- 
eration. 

llth  April,  1762. 


LETTER  CX. 

Why  do  the  Moon  and  the  Sun  appear  greater  at  rising 
and  setting  than  at  a  certain  Elevation  ?  Difficulties 
attending  the  Solution  of  this  Phenomenon, 

You  must  have  frequently  remarked,  that  the  moon 
at  rising  and  setting  appears  much  larger  than  when 
she  is  considerably  above  the  horizon ;  and  every 
one  must  give  testimony  to  the  truth  of  this  phenom- 
enon. The  same  observation  has  been  made  with 
respect  to  the  sun.  This  appearance  has  long  been 
a  stumbling-block  to  philosophers ;  and,  viewed  in 
whatever  light,  difficulties  almost  insuperable  pre- 
sent themselves. 

It  would  be  ridiculous  to  conclude  that  the 
moon's  body  is  really  greater  when  she  is  in  the 
horizon  than  when  she  has  attained  her  greatest 


MOON   AND    THE    SUN. 


389 


elevation.  For,  besides  that  such  an  idea  would  be 
absurd  in  itself,  it  must  be  considered,  that  when 
the  moon  appears  to  us  in  the  horizon  she  appears 
to  other  inhabitants  of  our  globe  more  elevated,  and 
consequently  smaller.  Now,  it  is  impossible  that 
the  same  body  should  be  at  the  same  time  greater 
and  smaller. 

It  would  be  almost  equally  ridiculous  to  attempt 
the  solution  of  this  strange  phenomenon  by  sup- 
posing that  the  moon  is  nearer  to  us  when  she  ap- 
pears in  the  horizon  than  when  she  is  arrived  at  a 
great  elevation,  from  our  certain  knowledge  that  a 
body  appears  greater  in  proportion  as  it  is  nearer 
us  ;  and  you  know  that  the  more  distant  any  object 
is,  the  smaller  it  appears.  It  is  for  this  reason  pre- 
cisely that  the  stars  appear  so  extremely  small, 
though  their  real  magnitude  be  prodigious. 

But  however  plausible  this  idea  may  seem,  it  is 
totally  destitute  of  foundation ;  for  it  is  undoubtedly 
certain,  that  the  moon  is  at  a  greater  distance  from 
us  at  rising  and  setting,  than  when  at  a  greater  ele- 
vation. The  demonstration  follows :  Fig.  200. 

Let  the  circle  A  B  D  be  the  earth, 
and  the  moon  at  L.  This  being  laid 
down,  an  inhabitant  at  A  will  see  the 
moon  in  his  zenith,  or  the  most  elevated 
point  of  the  heavens.  But  another 
inhabitant  at  D,  where  the  line  D  L 
touches  the  surface  of  the  earth,  will 
see  the  moon  at  the  same  time  in  his 
horizon ;  so  that  the  moon  will  appear, 
at  the  same  instant,  to  the  spectator  A 
in  his  zenith,  and  to  the  other  spectator 
D  in  his  horizon.  It  is  evident,  how- 
ever, that  the  last  distance  D  L  is 
greater  than  the  first  A  L,  and  conse- 
quently the  moon  is  more  distant  from 
those  who  see  her  in  the  horizon  than 
from  those  who  see  her  near  their 


Fig.  200. 


390      REFLECTIONS  RESPECTING  THE 

zenith.  Hence  it  clearly  follows,  that  the  moon, 
when  seen  in  the  horizon,  ought  to  appear  smaller, 
being  then  in  fact  farther  from  us  than  when  arrived 
at  a  great  elevation.  It  is  astonishing,  therefore, 
that  observation  should  be  in  direct  contradiction  to 
this,  and  that  the  moon  should  appear  much  greater 
when  viewed  near  the  horizon  than  in  the  summit 
of  the  heavens. 

The  more  this  phenomenon  is  investigated,  the 
more  strange  it  appears,  and  the  more  worthy  of  at- 
tention :  it  being  undoubtedly  certain  that  the  moon, 
when  most  remote,  that  is,  in  the  horizon,  ought  to 
appear  smaller,  whereas,  nevertheless,  every  one  is 
decidedly  of  opinion  that  she  then  appears  consid- 
erably greater.  This  contradiction  is  evident,  and 
even  seems  to  overturn  all  the  principles  laid  down 
in  optics,  which,  however,  are  as  clearly  demonstra- 
ble as  any  in  geometry. 

I  have  purposely  endeavoured  to  set  this  difficulty 
in  its  strongest  light,  in  order  to  make  you  the  more 
sensible  of  the  importance  of  the  true  solution. 
Without  entering  into  a  discussion  of  this  universal 
judgment,  formed  from  appearances,  respecting  the 
prodigious  magnitude  of  the  moon  in  the  horizon,  I 
shall  confine  myself  to  the  principal  question :  Is  it 
true,  in  fact,  that  the  moon,  when  near  the  horizon, 
actually  appears  greater  ? 

You  know  that  we  are  possessed  of  infallible 
means  of  exactly  measuring  the  heavenly  bodies,  by 
ascertaining  the  number  of  degrees  and  minutes 
which  they  occupy  in  the  heavens;  or,  which 
amounts  to  the  same  thing,  by  measuring,  Fig.  201, 
the  angle  EOF,  formed  by  the  lines  E  0  and  F  0, 

Fig.  201. 


MOON'S    APPARENT    MAGNITUDE.  391 

drawn  from  the  opposite  points  of  the  moon  to  the 
eye  of  the  spectator  0  ;  and  this  angle  E  O  F  is  what 
we  call  the  apparent  diameter  of  the  moon.  We 
have  likewise  instruments  perfectly  adapted  to  the 
purpose  of  exactly  determining  this  angle.  Now, 
when  we  employ  such  an  instrument  in  measuring 
the  moon's  diameter,  first  at  her  rising,  and  after- 
ward, when  she  has  gained  her  greatest  elevation, 
we  actually  find  her  diameter  somewhat  less  in  the 
first  case  than  in  the  other,  as  the  inequality  of  dis- 
tance requires.  There  cannot  remain  the  shadow 
of  doubt  as  to  this  ;  but,  for  that  very  reason,  the 
difficulty,  instead  of  diminishing,  gathers  strength  ; 
and  it  will  be  asked  with  so  much  the  more  eager- 
ness, How  comes  it  that  the  whole  world  agrees  in 
imagining  the  moon  to  be  greater  when  rising  or 
setting,  though  her  apparent  diameter  is  then  in 
reality  smaller  ]  and,  What  can  be  the  reason  of  this 
delusion,  to  which  men  are  universally  subject! 
The  astronomer,  who  knows  perfectly  well  that  the 
moon's  apparent  diameter  is  then  smaller,  falls  nev- 
ertheless into  the  same  deception  as  the  most  igno- 
rant clown. 

20th  April,  1762. 


t  LETTFR  CXI. 

Reflections  on  the  Question  respecting  the  Moon's  ap- 
parent Magnitude.  Progress  towards  a  Solution  of 
the  Difficulty.  Absurd  Explanations. 

You  would  scarcely  have  believed  that  the  simple 
appearance  of  the  moon  involved  so  many  difficul- 
ties ;  but  I  hope  I  shall  be  able  to  clear  the  way 
towards  a  solution,  by  the  following  reflections : — 

1.  It  is  not  astonishing  that  our  judgment  respect- 
ing the  magnitude  of  objects  should  not  always  be 
in  correspondence  with  the  visual  angle  under  which 


392      REFLECTIONS  RESPECTING  THE 

we  see  it :  of  this  daily  experience  furnishes  suffi- 
cient proof.  A  cat,  for  example,  appears,  when  very 
near,  under  a  greater  angle  than  an  ox  at  the  dis- 
tance of  100  paces.  I  could  never,  at  the  same  time, 
imagine  the  cat  to  be  larger  than  the  ox :  and  you 
will  please  to  recollect,  that  our  judgment  respecting 
magnitude  is  always  intimately  connected  with  that 
of  distance ;  so  that  if  we  commit  a  mistake  in  the 
calculation  of  distance,  our  judgment  respecting 
magnitude  becomes,  of  necessity,  erroneous. 

2.  In  order  to  elucidate  this  more  clearly,  it  some- 
times happens  that  a  fly  passing  suddenly  before  the 
eye,  without  our  thinking  of  it,  if  our  sight  is  fixed 
on  a  distant  object  we  imagine  at  first  that  the  fly  is 
at  a  great  distance ;  and  as  it  appears  under  a  very 
considerable  angle,  we  take  it  for  a  moment  to  be  a 
large  fowl,  which  at  the  proper  distance  would  ap- 
pear under  the  same  angle.     It  is  then  incontestably 
certain,  that  our  judgment  respecting  the  magnitude 
of  objects  is  not  regulated  by  the  visual  angle  under 
which  they  are  seen,  and  that  there  is  a  very  great 
difference  between  the  apparent  magnitude  of  objects 
and  the  calculated  or  computed  magnitude.     The 
first  is  regulated  by  the  visual  angle,  and  the  other 
depends  on  the  distance  to  which  we  suppose  the 
object  to  be  removed. 

3.  To  avail  myself  of  this  remark,  I  further  ob- 
serve, that  we  ought  not  to  say  that  we  see  the 
moon  greater  in  the  horizon  than  at  a  considerable 
elevation.     This  is  absolutely  false,  for  we  then  see 
her  even  somewhat  less.     But,  to  speak  accurately, 
we  ought  to  say  that  we  judge  and  compute  the 
moon  greater  when  she  is  in  the  horizon  ;  and  this 
is  literally  true  with  the  unanimous  consent  of  all 
mankind.    This  is  sufficient  to  reconcile  the  apparent 
contradiction  formerly  suggested ;  for  nothing  pre- 
vents our  judging  or  computing  the  moon  to  be 
greater  when  she  rises  or  sets,  though  she  is  seen 
under  a  smaller  visual  angle. 


MOON'S  APPARENT  MAGNITUDE.       393 

4.  We  are  no  longer,  then,  called  upon  to  explain 
why  we  see  the  moon  greater  in  the  horizon,  which 
is  impossible,  for  in  reality  she  then  appears  smaller, 
as  may  be  demonstrated  by  measuring  the  visual 
angle.     The  difficulty,  therefore,  is  reduced  to  this : 
Wherefore  do  we  judge  or  compute  the  moon  to  be 
greater  when  in  those  situations'?   or  rather,  we 
must  endeavour  to  account  for  this  whimsical  com- 
putation.    The  thing  is  not  surprising  in  itself,  as 
we  know  a  thousand  cases  in  which  we  estimate 
objects  to  be  very  great,  though  we  see  them  under 
very  small  angles. 

5.  We  have  only  to  say,  then,  that  when  the 
moon  is  rising  or  setting,  we  suppose  her  to  be  at  a 
greater  distance  than  when  she  has  attained  a  cer- 
tain elevation.     Whenever  this  computation  is  set- 
tled, whatever  may  be  the  cause  of  it,  the  conse- 
quence is  necessary,  that  we  must  b'kewise  conclude 
the  moon  to  be  greater  in  proportion.     For,  in  every 
case,  the  more  distant  we  estimate  any  object  to  be, 
the  greater  we  presume  it  is,  and  this  in  the  same 
proportion.     As  soon  as  I  imagine,  by  whatever 
illusion,  that  a  fly  passing  close  before  my  eye  is  at 
the  distance  of  100  paces,  I  am  obliged,  almost 
whether  I  will  or  not,  to  suppose  it  as  many  times 
greater  as  100  paces  exceed  the  real  distance  of  the 
fly  from  my  eyes. 

6.  We   are  now,  therefore,  reduced  to  a  new 
question :  Wherefore  do  we  presume  that  the  moon 
is  at  a  greater  distance  when  she  is  seen  in  the 
horizon  1  and,  Wherefore  is  this  illusion  so  universal 
as  not  to  admit  of  a  single  exception !    For  the  illu- 
sion of  imagining  that  the  moon  is  then  at  a  much 
greater  distance  is  altogether  unaccountable.     It  is 
undoubtedly  true  that  the  moon  is  then  really  a  little 
more  distant,  as  I  demonstrated  in  my  last  Letter ; 
but  the  difference  is  so  trifling  as  to  be  impercepti- 
ble.    Besides,  the  sun,  though  100  times  more  dis- 
tant than  the  moon,  does  not  appear  so,  and  the  eye 


394  APPEARANCE    OF    THE    MOON 

estimates  even  the  fixed  stars  as  nearly  at  the  same 
distance. 

7.  Though,  therefore,  when  the  moon  is  in  the 
horizon,  she  is  actually  a  little  more  distant,  this 
circumstance   cannot   affect  the  present  question ; 
and  this  universal  computation,  which  induces  the 
whole  world  to  imagine  the  moon  to  be  then  at  a 
much  greater  distance  than  she  really  is,  must  be 
founded  on  reasons  entirely  different,  and  capable 
of  producing  universal  illusion.     For,  as  the  com- 
putation is  unquestionably  erroneous,  the  reasons 
which  determine  us  to  make  it  must  necessarily  be 
very  striking. 

8.  Some  philosophers  have  attempted  to  explain 
this  phenomenon  by  alleging  that  it  is  occasioned 
by  the  intervention  of  various  objects  between  us 
and  the  moon,  such  as  cities,  villages,  forests,  and 
mountains.     This,  say  they,  is  the  reason  that  she 
then  appears  to  be  much  farther  off;  whereas,  when 
she  has  attained  a  considerable  elevation,  as  no  other 
body  intervenes,  she  must  appear  to  be  nearer.    But 
this  explanation,  however  ingenious  it  may  at  first 
sight  appear,  is  destitute  of  solidity.     On  looking  at 
the  moon  in  the  horizon  through  a  small  aperture 
made  in  any  body  which  shall  conceal  the  interme- 
diate objects,  she  nevertheless  still  seems  greater. 
Besides,  we  do  not  always  imagine  that   objects 
between  which  and  us  many  other  bodies  interpose 
are  more  distant.     A  great  hall,  for  example,  when 
quite  empty,  usually  appears  much  larger  than  when 
filled  with  company,  notwithstanding  the  numerous 
objects  then  interposed  between  us  and  the  walls  of 
the  apartment. 

24th  April,  1762. 


IN   THE    HORIZON.  395 


LETTER  CXII. 

An  Attempt  towards  the  true  Explanation  of  this  Phe- 
nomenon,— The  Moon  appears  more  distant  when  in 
the  Horizon  than  when  at  a  great  Elevation. 

WE  are  still,  then,  very  far  from  the  true  solu- 
tion of  this  universal  illusion,  under  which  all, 
without  exception,  are  induced  to  imagine  the  moon 
to  be  much  greater  when  in  the  horizon  than  when 
considerably  elevated.  I  have  already  remarked, 
that  this  phenomenon  is  so  much  the  more  unac- 
countable, from  its  being  demonstrable  tf.iat  the 
moon's  apparent  diameter  is  then  even  somewhat 
less  :  we  ought  not,  therefore,  to  say,  that  we  then 
see  the  moon  greater,  but  that  we  imagine  her  to 
be  so. 

Accordingly,  I  have  very  often  observed  our  judg- 
ment of  objects  to  differ  very  widely  from  vision 
itself.  We  do  not  hesitate,  for  example,  to  conclude 
that  a  horse  100  paces  distant  is  larger  than  a  dog 
one  pace  distant,  though  the  apparent  magnitude  of 
the  dog  is  unquestionably  greater;  or,  which  amounts 
to  the  same  thing,  though  the  image  of  the  dog 
painted  on  the  bottom  of  the  eye  be  greater  than 
that  of  the  horse.  Our  judgment  in  this  case  is 
regulated  by  taking  distance  into  the  account ;  and 
laying  it  down  that  the  horse  is  much  farther  off 
than  the  dog,  we  conclude  he  is  much  larger. 

It  is  very  probable,  therefore,  that  the  same  cir- 
cumstance may  take  place  respecting  the  moon's 
appearance,  and  induce  us  to  reckon  the  moon 
greater  when  in  the  horizon  than  at  a  considerable 
elevation.  In  the  case  of  the  horse,  our  computa- 
tion of  distance  was  founded  in  truth  ;  but  here,  as 
it  is  absolutely  erroneous,  the  illusion  must  be  sin- 
gularly unaccountable,  but  must,  at  the  same  time, 


396  APPEARANCE    OF    THE    MOON 

have  a  certain  foundation,  as  its  prevalence  is  uni- 
versal, and  cannot  therefore  be  imputed  to  caprice. 
Wherein  can  it  consist  ]  This  is  to  be  the  subject 
of  our  present  inquiry. 

1.  Every  one  considers   the   azure   expanse  of 
heaven  as  a  flattened  arch,  the  summit  of  which  is 
much  nearer  to  us  than  the  under  part,  where  it 
meets  the  horizon.     A  person,  accordingly,  stand- 
ing- on  a  plane  A  B,  Fig.  202,  p^,  202. 
which  extends  as  far   as  his 

sight,  perceives   the  vault  of 

heaven,  commonly  called  the  -A-  c 

firmament,    under    the    figure 

A  E  F  B,  in  which  the  distances  C  A  and  C  B  are 

much  gi eater  than  from  the  zenith  to  C. 

2.  This  idea  is  likewise  beyond  all  question  a 
mere  illusion,  there  being  in  reality  no  such  vault 
surrounding  and  enclosing  us  on  every  side.     It  is 
a  void  of  immense  extent,  as  it  reaches  to  the  most 
distant  of  the  fixed  stars — an  interval  that  far  ex- 
ceeds all  power  of  imagination.     I  use  the  word 
void,  to  distinguish  it  from  gross  terrestrial  bodies. 
For,  near  the  earth,  space  is  occupied  by  our  at- 
mosphere ;  and  beyond,  by  that  fluid,  infinitely  more 
subtile,  which  we  call  ether. 

3.  Though  this  vault,  however,  has  no  real  exist- 
ence, it  possesses  an  undoubted  reality  in  our  imagi- 
nation ;  and  all  mankind,  the  philosopher  as  well  as 
the  clown,  are  subject  to  the  same  illusion.     On  the 
surface  of  *his  arch  we  imagine  the  sun,  the  moon, 
and  all  the  stars  to  be  disposed  like  so  many  bril- 
liant studs  affixed  to  it ;  and  though  we  have  a  per- 
fect conviction  of  the   contrary,   we  cannot  help 
giving  way  to  the  illusion. 

4.  This  being  laid  down,  when  the  moon  is  in  the 
horizon,  imagination  attaches  her  to  the  point  A  or 
B  of  this  supposed  vault,  and  hence  we  conclude  her 
distance  to  be  as  much  greater  as  we  consider  the 
line  C  A  or  C  B  to  be  greater  than  C  Z  ;  but  when 


IN    THE    HORIZON.  397 

she  ascends  and  approaches  the  zenith,  we  imagine 
she  comes  nearer;  and  if  she  reaches  the  very 
zenith,  we  think  she  is  at  the  least  possible  distance. 

5.  The  illusion  as  to  distance  necessarily  involves 
that  which  respects  magnitude.     As  the  moon  at  A 
appears  much  farther  from  C  than  in  the  zenith, 
we  are  in  a  manner  forced  to  conclude  that  the  moon 
is  really  so  much  greater;  and  that  in  the  same 
proportion  that  the  distance  C  A  appears  to  exceed 
the  distance  C  Z.    All  will  not,  perhaps,  agree  in 
determining  this  proportion ;  one  will  say,  the  moon 
appears  to  him  twice  as  great  when  in  the  horizon ; 
another  will  say  three  times;  and  the  generality 
will  declare  for  the  medium  between  two  and  three; 
but  every  one  will  infallibly  agree  in  asserting  that 
the  moon  appears  larger. 

6.  It  may  be  necessary  here  to  present  you  with 
the  demonstration  of  this  proposition.     The  com- 
putation of  magnitude  is  necessarily  involved  in  the 
computation  of  distance.    When  the  moon  is  near 
the  horizon,  we  see  her.  Fig.  203,  under  a  certain 
angle,  say  MCA,  the  spec-  p.     Q  „ 
tator  being  at  C ;  and  when 

she  is  at  a  very  great  eleva- 
tion, let  N  C  D  be  the  angle 
under  which  we  see  her.  It 
is  evident  that  these  two  an- 
gles  M  C  A  and  N  C  D  are 
nearly  equal  to  each  other,  the  difference  being  im- 
perceptible. 

7.  But,  in  the  first  case,  as  we  estimate  the  moon's 
distance  to  be  much  greater,  or  equal  to  the  line 
C  A,  with  reference  to  the  imaginary  vault  above 
described,  it  follows,  that  we  compute  the  moon's 
diameter  to  be  equal  to  the  line  M  A.     But,  in  the 
other  case,  the  distance  of  the  moon  C  D  appears 
much  smaller;  and  consequently,  as  the  angle  N  C  D 
is  equal  to  the  angle  MCA,  the  computed  magni- 

VOL.  IL— L  1 


398       APPEARANCE  OF  THE  HEAVENS 

tude  D  N  will  be  much  smaller  than  the  computed 
magnitude  A  M. 

8.  To  put  this  beyond  a  doubt,  you  have  only  to 
cut  off  from  the  lines  C  M  and  C  A  the  parts  C  d 
and  C  n,  equal  to  the  lines  C  D  and  C  N ;  and  as  in 
the  two  triangles  C  d  n  and  C  D  N,  the  angles  at  the 
point  C  are  equal,  the  triangles  themselves  are  like- 
wise so,  and  consequently  the  line  D  N  will  be  equal 
to  the  line  d  n ;  but  d  n  is  evidently  smaller  than 
A  M,  and  that  as  many  times  as  the  distance  C  d 
and  C  D  is  less  than  C  A.  This  is  a  clear  demon- 
stration of  the  reason  why  we  estimate  the  moon 
to  be  greater  when  in  the  horizon  than  when  near 
the  zenith. 

29th  April,  1762. 


LETTER  CXIII. 

The  Heavens  appear  under  the  form  of  an  Arch  flattened 
towards  the  Zenith. 

You  will  charge  me,  no  doubt,  with  pretending  to 
explain  one  illusion  by  another  equally  unaccount- 
able. It  may  be  said,  that  the  imaginary  vault  of 
heaven  is  altogether  as  inconceivable  as  the  in- 
creased appearance  of  the  moon  and  the  other  hea- 
venly bodies  when  in  or  near  the  horizon.  The 
objection  is  not  without  foundation,  and  therefore 
lays  me  under  the  necessity  of  attempting  to  explain 
the  true  reason  why  the  heavens  appear  in  the  form 
of  an  arch  flattened  towards  the  summit.  The  fol- 
lowing reflections  may,  perhaps,  be  received  as  an 
acquittance  of  my  engagement. 

1.  In  order  to  account  for  this  imaginary  vault,  it 
will  be  alleged  that  it  proceeds  from  the  appearance 
of  the  heavenly  bodies,  as  seeming  more  remote 
when  in  the  horizon  than  when  near  to  or  in  the 
zenith.  This  is  undoubtedly  a  formal  petitio  prin- 


TOWARDS    THE    ZENITH.  399 

cipii,  as  logicians  call  it,  or  a  begging  of  the  ques- 
tion, which  every  one  is  entitled  to  reject  as  a 
ground  of  reasoning.  In  truth,  having  said  above 
that  the  imaginary  vault  of  heaven  makes  the  moon 
in  the  horizon  appear  farther  off  than  when  near 
the  zenith,  it  would  be  ridiculous  to  affirm,  that  the 
thing  which  leads  us  to  imagine  the  existence  of 
such  a  vault  is  that  horizontal  objects  appear  more 
distant  than  vertical. 

2.  It  was  not,  however,  useless  to  suggest  the 
idea  of  this  imaginary  vault,  though  it  may  not 
carry  us  a  great  way  forward;   and  after  I  shall 
have  explained  wherefore  the  heavenly  bodies  ap- 
pear more  remote  when  viewed  near  the  horizon, 
you  will  be  enabled  to  comprehend,  at  the  same  time, 
the  reason  of  that  twofold  universal  illusion,  namely, 
the  apparently  increased  magnitude  of  the  heavenly 
bodies  when  in  the  horizon,  and  the  flattened  arch 
of  heaven. 

3.  The  whole,  then,  reverts  to  this,  to  explain 
wherefore  the  heavenly  bodies  when  seen  in  the 
horizon  appear  more  remote  than  when  at  a  con- 
siderable elevation.      I  now  affirm,  it  is  because 
these  objects  appear  less  brilliant ;  and  this  imposes 
on  me  the  double  task  of  demonstrating  why  these 
objects  display  less  brilliancy  when  in  or  near  the 
horizon,  and  of  explaining  how  this  circumstance 
necessarily  involves  the  idea  of  a  greater  distance. 
I  flatter  myself  I  shall  be  enabled  to  discharge  both 
of  these  to  your  satisfaction. 

4.  The  phenomenon  itself  will  not  be  called  in 
question.     However  greater  the  sun's  lustre  may  be 
at  noon,  which  it  is  then  impossible  to  ascertain, 
you  know  that  in  the  morning  and  evening,  when 
he  is  rising  or  setting,  it  is  possible  to  contemplate 
his  body  without  any  injury  to  the  eye ;  and  the 
same  thing  takes  place  with  respect  to  the  moon 
and  all  the  stars,  whose  brilliancy  is  greatly  dimin- 
ished in  the  vicinity  of  the  horizon.    We  accord- 


400      APPEARANCE  OF  THE  HEAVENS. 

ingly  do  not  see  the  smaller  stars  when  at  a  small 
elevation  above  the  horizon,  though  they  are  suf- 
ficiently discernible  at  a  certain  height. 

5.  This  being  established  beyond  a  possibility  of 
doubt,  the  cause  of  this  difference  of  illumination 
remains  to  be  investigated.     It  is  abundantly  evident 
that  we  can  trace  it  only  in  our  atmosphere,  or  the 
body  of  air  which  encompasses  our  earth,  in  so  far 
as  it  is  not  perfectly  transparent.     For  if  it  were, 
so  that  all  the  rays  should  be  transmitted  through 
it  without  undergoing  any  diminution,  there  could 
be  no  room  to  doubt  that  the  stars  must  always 
shine  with  the  same  lustre,  in  whatever  region  of 
the  heavens  they  might  be  discovered. 

6.  But  the  air,  a  substance  much  less  fine  and 
subtile  than  ether,  whose  transparency  is  perfect, 
is  continually  loaded  with  heterogeneous  particles, 
rising  into  it  above  the  earth,  such  as  vapours  and 
exhalations,  which  destroy  its  transparency ;  so  that 
if  a  ray  should  fall  in  with  such  a  particle,  it  would 
be  intercepted,  and  almost  extinguished  by  it.     It  is 
accordingly  evident,  that  the  more  the  air  is  loaded 
with  such  particles,  which  prevent  the  transmission 
of  light,  the  more  rays  must  be  lost  by  the  intercep- 
tion ;  and  you  know  that  a  very  thick  mist  deprives 
the  air  of  almost  all  its  transparency,  to  such  a  de- 
gree that  it  is  frequently  impossible  to  distinguish 
objects  at  three  paces'  distance. 

7.  Let  the  points  marked  in  Fig.  204  represent 

Fig.  204. 


*«££ 


such  particles  scattered  througti  the  air,  whose 
number  is  greater  or  less,  according  as  the  air  is 
more  or  less  transparent.  It  is  evident,  that  many 


LIGHT    OF    THE    HEAVENLY    BODIES.  401 

of  the  rays  which  pervade  that  space  must  be  lost, 
and  that  the  loss  must  be  greater  in  proportion  as 
the  space  which  they  had  to  run  through  that  air 
is  greater.  We  see,  then,  that  distant  objects  be- 
come invisible  in  a  fog,  while  such  as  are  very  near 
the  eye  may  be  still  perceptible,  because  the  rays 
of  the  first  meet  in  their  progress  a  greater  number 
of  particles  which  obstruct  their  transmission. 

8.  We  must  hence  conclude,  that  the  longer  the 
space  is  through  which  the  rays  of  the  heavenly 
bodies  have  to  pass  through  the  atmosphere  in  order 
to  reach  our  eyes,  the  more  considerable  must  be 
their  loss  or  diminution.  Of  this  you  can  no  longer 
entertain  any  doubt.  All  that  remains,  then,  is 
simply  to  demonstrate,  that  the  rays  of  the  stars 
which  we  see  in  or  near  our  horizon  have  a  longer 
space  of  the  atmosphere  to  pervade  than  when  nearer 
the  zenith.  When  this  is  done,  you  will  easily 
comprehend  why  the  heavenly  bodies  appear  much 
less  brilliant  when  near  the  horizon  than  at  the  time 
of  rising  and  setting.  This  shall  be  the  subject  of 
my  next  Letter. 

1st  May,  1762. 


LETTER  CXIV. 

Reason  assigned  for  the  Faintness  of  the  Light  of  the 
Heavenly  Bodies  in  the  Horizon. 

WHAT  I  have  just  advanced,  namely,  that  the  rays 
of  the  heavenly  bodies,  when  in  the  horizon,  have  a 
larger  portion  of  our  atmosphere  to  pervade,  may 
appear  somewhat  paradoxical,  considering  that  the 
atmosphere  universally  extends  to  the  same  height, 
so  that  at  whatever  point  the  star  may  be,  its  rays 
must  always  penetrate  through  the  whole  of  that 
height  before  it  can  reach  our  eyes.  The  following 
L19 


402 


LIGHT    OF    THE    HEAVENLY    BODIES 


205. 


reflections,  I  flatter  myself,  will  give  you  complete 
satisfaction  on  the  subject. 

1.  It  is  first  of  all  necessary  to  form  a  just  idea 
of  the  atmosphere  which  surrounds  our  globe.     For 
this    purpose    the    interior  circle 

A  B  C  D,  Fig.  205,  shall  represent 
the  earth,  and  the  exterior  dotted 
circle  abed  shall  mark  the  height 
of  the  atmosphere.  Let  it  be  re- 
marked, that  universally  in  propor- 
tion as  the  air  rises  above  the  sur- 
face of  the  earth  it  becomes  always 
more  transparent  and  subtile,  so 
that  at  last  it  is  imperceptibly  lost 
in  the  ether  which  fills  the  whole  expanse  of  heaven. 

2.  The  grosser  air,  that  which  is  most  loaded  with 
the  particles  that  intercept  and  extinguish  the  rays 
of  light,  is  universally  found  in  the  lower  regions, 
near  the  surface  of  the  earth.     It  becomes,  there- 
fore, more  subtile  as  we  ascend,  and  less  obstructive 
of  the  light ;  and  at  the  height  of  5  English  miles 
has  become  so  transparent  as  to  occasion  no  per- 
ceptible obstruction  whatever  of  the  light.     The 
distance,  then,  between  the  interior  circle  and  the 
exterior,  may  be  fixed  at  5  English  miles  nearly, 
whereas  the  semi-diameter  of  the  globe  contains 
<ibout  3982  of  such  miles ;  so  that  the  height  of  the 
atmosphere  is  a  very  small  matter  compared  with 
the  magnitude  of  the  globe. 

3.  Let  us  now  con- 


sider, Fig.  206,  a  spec- 
tator at  A,  on  the  surface 
of  the  earth ;  and  draw- 
ing from  the  centre  of 
the  globe  G,  through  A, 
the  line  G  Z,  it  will  be 
directed  towards  the  ze- 
nith of  the  spectator. 
The  line  A  S,  which  is 


Fig.  206. 


IN  THE    HORIZON.  403 

perpendicular,  and  touches  the  earth,  will  be  hori- 
zontal to  it.  Consequently,  he  will  see  a  star  at  Z 
in  his  zenith,  or  in  the  summit  of  the  heavens  ;  but  a 
star  at  S  will  appear  to  him  in  the  horizon  at  its 
rising  or  setting.  Each  of  these  stars  may  be  con- 
sidered as  infinitely  distant  from  the  earth,  though  it 
was  impossible  to  represent  this  in  the  figure. 

4.  Now  you  have  only  to  cast  your  eye  once  more 
on  the  figure,  to  be  satisfied  that  the  rays  proceeding 
from  S  have  a  much  longer  space  to  travel  through 
the  atmosphere  than  those  from  the  star  Z,  before 
they  reach  the  spectator  at  A.     Those  from  the 
star  Z  have  only  to  pass  through  the  perpendicular 
height  of  the  atmosphere  a  A,  which  is  not  above  5 
English  miles,  whereas  those  that  come  from  the 
star  S  have  to  travel  the  whole  space  h  A,  which  is 
evidently  much    longer;    and  could  the  figure  be 
represented  more  conformably  to  the  fact,  so  as  to 
exhibit  the  radius  G  A  3982  times  longer  than  the 
height  A  a,  we  should  find  the  distance  A  A  to  exceed 
40  such  miles. 

5.  It  is  further  of  importance  to  remark,  that  the 
rays  of  the  star  Z  have  but  a  very  small  space  to 
travel  through  the  lower  region  of  the  atmosphere, 
which  is  most  loaded  with  vapour ;  whereas  the  rays 
of  the  star  S  have  a  much  longer  course  to  perform 
through  that  region,  and  are  obliged  to  graze,  if  I  may 
use  the  expression,  along  the  surface  of  the  earth. 
The  conclusion,  then,  is  obvious.     The  rays  of  the 
star  Z  undergo  scarcely  any  diminution  of  lustre, 
but  those  of  the  star  S  must  be  almost  extinguished, 
from  so  long  a  passage  through  the  grosser  air. 

6.  It  is  indisputably  certain,  then,  that  the  stars 
which  we  see  in  the  horizon  must  appear  with  a 
lustre   extremely  diminished ;   and  it  will   simply 
account  to  you  for  a  well-known  fact,  that  you  can, 
without  any  inconvenience,  fix  your  eyes  steadily 
on  the  rising  or  setting  sun ;  whereas,  at  noon,  or 
at  a  considerable  elevation,  his  lustre  is  insupport- 


404  LIGHT   OF   THE    HEAVENLY  BODIES. 

able.  This  is  the  first  point  I  undertook  to  demon- 
strate ;  I  proceed  to  the  second,  namely,  to  prove 
that  it  is  the  diminution  of  light  which  forces  us 
almost  to  imagine  the  heavenly  bodies  at  a  much 
greater  distance  than  when  we  see  them  in  all  their 
lustre. 

7.  The  reason  must  be  sought  in  terrestrial  bodies, 
with  which  we  are  every  day  conversant,  and  re- 
specting whose  distance  we  form  a  judgment.     But 
for  the  same  reason  that  rays  of  light  in  passing 
through  the  air  undergo  some  diminution  of  lustre, 
it  is  evident  that  the  farther  an  object  is  removed 
from  us,  the  more  of  its  lustre  it  loses,  and  the  more 
obscure  it  becomes  in  proportion.     Thus,  a  very  dis- 
tant mountain  appears  quite  dark ;  but  on  a  nearer 
approach  we  can  easily  discover  trees  on  it,  and 
other  minuter  objects,  which  it  was  impossible  to 
distinguish  at  a  very  remote  distance. 

8.  This  observation,  so  general,  and  which  never 
misleads  us  in  contemplating  terrestrial  bodies,  has 
produced  in  us  from  our  childhood  this  fundamental 
principle,  from  which  we  conclude  objects  to  be 
distant  in  proportion  as  the  rays  of  light  which  they 
emit  are  weakened.     It  is  in  virtue  of  this  principle, 
therefore,  that  we  conclude  the  moon  to  be  farther 
off  at  rising  and  setting  than  at  a  considerable  eleva- 
tion ;    and  for  the  same  reason  we  conclude  she  is 
so  much  greater.     You  will,  I  flatter  myself,  admit 
this  reasoning  to  be  solid,  and  this  embarrassing  phe- 
nomenon to  be  as  clearly  elucidated  as  the  nature 
of  the  subject  permits. 

4th  May,  1762. 


THE   DISTANCE    OF    OBJECTS.  405 


LETTER  CXV. 

Illusion  respecting  the  Distance  of  Objects,  and  the 
Diminution  of  Lustre. 

THE  principle  of  our  imagination,  by  which  I  have 
endeavoured  to  explain  the  phenomenon  of  the 
moon's  greater  apparent  magnitude  in  the  horizon 
than  at  a  considerable  elevation,  is  so  deeply  rooted 
in  our  nature  as  to  become  the  source  of  a  thousand 
similar  illusions,  some  of  which  I  will  take  the  liberty 
to  suggest. 

We  have  been  habituated  from  infancy,  almost 
involuntarily,  to  imagine  objects  to  be  distant  in 
proportion  as  their  lustre  is  diminished ;  and,  on  the 
other  hand,  very  brilliant  objects  appear  to  be  nearer 
than  they  really  are.  This  illusion  can  proceed  only 
from  an  ill-regulated  imagination,  which  very  fre- 
quently misleads  us.  It  is  nevertheless  so  natural 
and  so  universal  that  no  one  is  capable  of  guarding 
against  it,  though  the  error,  in  many  cases,  is  ex- 
tremely palpable,  as  I  have  shown  in  the  instance 
of  the  moon ;  but  we  are  equally  deceived  in  a  va- 
riety of  other  instances,  as  I  shall  presently  make 
appear. 

1.  It  is  a  well-known  illusion  that  the  flame  of  a 
conflagration  in  the  night  appears  much  nearer  than 
it  really  is.    The  reason  is  obvious  ;  the  fire  blazes 
in  all  its  lustre  ;  and  in  conformity  to  a  principle  pre- 
established  in  the  imagination,  we  always  conclude 
it  to  be  nearer  than  it  is  in  reality. 

2.  For  the  same  reason  a  great  hall,  the  walls  of 
which  are  perfectly  white,  always  appears  smaller. 
White,  you  know,  is  the  most  brilliant  colour :  hence 
we  conclude  the  walls  of  such  an  apartment  to  be  too 
near ;  and  consequently  the  apparent  magnitude  is 
thereby  diminished. 


406  THE    DISTANCE    OF    OBJECTS. 

3.  But  in  an  apartment  hung  with  black,  as  is  the 
custom  in  mournings,  we   perceive  the   directly 
opposite  effect.     The  apartment  now  appears  con- 
siderably more  spacious  than  it  really  is.     Black 
is  undeniably  the  most  gloomy  of  colours,  for  it 
reflects  scarcely  any  light  on  the  eye ;  hence  the 
walls  of  an  apartment  in  deep  mourning  seem  more 
distant  than  they  are,  and  consequently  greater ;  but 
let  the  black  hangings  be  removed  and  the  white 
colour  reappear,  and  the  apartment  will  seem  con- 
tracted. 

4.  No  class  of  men  avail  themselves  more  of  this 
natural  and  universal  illusion  than  painters.     The 
same  picture,  you  know,  represents  some  objects  as 
at  a  great  distance,  and  others  as  very  near ;  and 
here  the  skill  of  the  artist  is  most  conspicuous.     It 
is  not  a  little  surprising,  that  though  we  know  to 
absolute  certainty  all  the  representations  of  a  pic- 
ture to  be  expressed  on  the  same  surface,  and  con- 
sequently at  nearly  the  same  distance  from  the  eye, 
we  should  be,  nevertheless,  under  the  power  of  illu- 
sion, and  imagine  some  to  be  quite  near,  and  others 
extremely  distant.     This  illusion  is  commonly  as- 
cribed to  a  dexterous  management  of  light  and  shade, 
which  undoubtedly  furnish  the  painter  with  endless 
resources.     But  you  have  only  to  look  at  a  picture 
to  be  sensible  that  the  objects  intended  to  be  thrown 
to  a  great  distance  are  but  faintly  and  even  indis- 
tinctly expressed.     Thus,  when  the  eye  is  directed 
to  very  remote  objects,  we  easily  perceive,  for  ex- 
ample, that  they  are  men ;  but  it  is  impossible  to 
distinguish  the  parts,  such  as  the  eyes,  the  nose,  the 
mouth;  and  it  is  in  conformity  to  this  appearance 
that  the  painter  represents  objects.    But  those  which 
he  intends  should  appear  close  to  us  he  displays  in 
all  the  brightness  of  colouring,  and  is  at  pains  clearly 
to  express  each  minute  particular.     If  they  are  per- 
sons, we  can  distinguish  the  smallest  lineaments  of 
the  face,  the  folds  of  the  drapery,  &c. :  this  part 


AZURE  COLOUR  OF  THE  HEAVENS.     407 

of  the  representation  seems,  I  may  say,  to  rise  out 
of  the  canvass,  while  other  parts  appear  to  sink  and 
retire. 

5.  On  this  illusion,  therefore,  the  whole  art  of 
painting  entirely  rests.  Were  we  accustomed  to 
form  our  judgment  in  strict  conformity  to  truth,  this 
art  would  make  no  more  impression  on  us  than  if 
we  were  blind.  To  no  purpose  would  the  painter 
call  forth  all  his  powers  of  genius,  and  employ  the 
happiest  arrangement  of  colours  ;  we  should  coldly 
affirm,  on  that  piece  of  canvass  there  is  a  red  spot, 
here  a  blue  one  ;  there  a  black  stroke,  here  some 
whitish  lines ;  every  thing  is  on  the  same  plane  sur- 
face ;  there  is  no  rising  nor  sinking ;  therefore  no 
real  object  can  be  represented  in  this  manner :  the 
whole  would  in  this  case  be  considered  as  a  scrawl- 
ing on  paper,  and  we  should  perhaps  fatigue  ourselves 
to  no  purpose  in  attempting  to  decipher  the  meaning 
of  all  these  different  coloured  spots.  Would  not  a 
man  in  such  a  state  of  perfection  be  an  object  of 
much  compassion,  thus  deprived  of  the  pleasure 
resulting  from  the  productions  of  an  art  at  once  so 
amusing  and  so  instructive  1 

8th  May,  1762. 


LETTER  CXVI. 

On  the  Azure  Colour  of  the  Heavens. 

You  are  now  enabled  to  comprehend  the  reason 
why  the  sun  and  moon  appear  much  greater  when 
in  the  horizon  than  at  a  considerable  elevation.  It 
consists  in  this,  that  we  then  unintentionally  com- 
pute these  bodies  to  be  at  a  greater  distance,  a  com- 
putation founded  on  the  very  considerable  diminution 
which  their  lustre  in  that  position  undergoes,  from 
the  longer  passage  which  the  rays  have  to  force 
through  the  lower  region  of  the  atmosphere,  which 


408  ON   THE    AZURE    COLOUR 

is  the  most  loaded  with  vapours  and  exhalations, 
whereby  the  transparency  is  diminished.  This  is  a 
brief  recapitulation  of  the  reflections  which  I  have 
taken  the  liberty  to  suggest  on  this  subject. 

This  quality  of  the  air,  which  diminishes  transpa- 
rency, might  at  first  sight  be  considered  as  a  defect. 
But  on  attending  to  consequences,  we  shall  find  it  so 
far  from  being  such,  that  we  ought,  on  the  contrary, 
to  acknowledge  in  it  the  infinite  wisdom  and  good- 
ness of  the  CREATOR.  To  this  impurity  of  the  air 
we  are  indebted  for  that  wonderful  and  ravishing 
spectacle  which  the  azure  of  the  heavens  presents 
to  the  eye  ;  for  the  opaque  particles  which  obstruct 
the  rays  of  light  are  illuminated  by  them,  and  after- 
ward retransmit  their  own  proper  rays,  produced  in 
their  surface  by  a  violent  agitation,  as  is  the  case  in 
all  opaque  bodies.  Now,  it  is  the  number  of  vibra- 
tions communicated  to  them  which  represents  to  us 
this  magnificent  azure  ;  a  circumstance  which  well 
deserves  to  be  completely  unfolded. 

1.  I  observe,  first,  that  these  particles  are  ex- 
tremely minute  and  considerably  distant  from  each 
other,  besides  their  being  delicately  fine  and  almost 
wholly  transparent.  Hence  it  comes  to  pass,  that 
each  separately  is  absolutely  imperceptible,  so  that 
we  can  be  affected  by  them  only  when  a  very  great 
number  transmit  their  rays  at  once  to  the  eye,  and 
nearly  in  the  same  direction.  The  rays  of  several 
must  therefore  be  collected,  in  order  to  excite  a  sen- 
sation. 

2.  Hence  it  clearly  follows,  that  such  of  these 
particles  as  are  near  to  us  escape  our  senses,  for  they 
must  be  considered  as  points  dispersed  through  the 
mass  of  air. 

But  such  as  are  very  distant  from  the  eye,  as, 
Fig.  207,  the  points  a  b  c,  col-  „. 

lect  in  the  eye  O,  almost  ac-  • 

cording  to  the  same  direction,      o-* 
their  several  rays,  which  thus 


OF    THE    HEAVENS.  409 

become  sufficiently  strong  to  affect  the  sight,  espe- 
cially when  it  is  considered  that  similar  particles 
more  remote,  efg  h,  as  well  as  others  more  near, 
concur  in  producing  this  effect. 

3.  The  azure  colour  which  we  see  in  the  heavens 
when  serene  is  nothing  else,  then,  but  the  result  of 
all  these  particles  dispersed  through  the  atmosphere, 
especially  of  such  as  are  very  remote  :  it  may  be 
affirmed,  therefore,  that  they  are  in  their  nature  blue, 
but  a  blue  extremely  clear,  which  does  not  become 
sufficiently  deep  and  perceptible,  except  when  they 
are  in  a  very  great  number,  and  unite  their  rays  ac- 
cording to  the  same  direction. 

4.  Art  has  the  power  of  producing  a  similar  effect. 
If,  on  dissolving  a  small  quantity  of  indigo  in  a  great 
quantity  of  water,  you  let  that  water  fall  drop  by  drop, 
you  will  not  perceive  in  the  separate  drops  the 
slightest  appearance  of  colour ;  and  on  pouring  some 
of  it  into  a  small  goblet,  y9u  will  perceive  only  a 
faint  bluish  colour.     But  if*  you  fill  a  large  vessel 
with  the  same  water,  and  view  it  at  a  distance,  you 
will  perceive  a  very  deep  blue.     The  same  experi- 
ment may  be  made  with  other  colours.     Burgundy 
wine,  in  very  small  quantities,  appears  only  to  be 
faintly  reddish ;  but  in  a  large  flask  completely  filled, 
the  wine  appears  of  a  deep  red. 

5.  Water,  in  a  large  and  deep  vessel,  presents 
something  like  colour ;  but  in  a  small  quantity  is 
altogether  clear  and  limpid.     This  colour  is  com- 
monly more  or  less  of  a  greenish  cast,  which  may 
warrant  us  in  saying  that  the  minute  particles  of 
water  are  likewise  so,  but  of  a  colour  so  delicately 
fine  that  a  great  mass  of  it  must  be  collected  before 
the  colour  can  be  perceptible,  because  the  rays  of  a 
multitude  of  particles  then  concur  towards  producing 
this  effect. 

6.  As  it  appears  probable,  from  this  observation, 
that  the  minute  particles  of  water  are  greenish,  it 
might  be  maintained,  that  the  reason  why  the  sea, 

VOL.  II.— M  m 


410  OF    TRANSPARENT    AIR. 

or  the  water  of  a  lake  or  a  pool,  appears  green,  is  the 
very  same  that  gives  the  heavens  the  appearance  of 
azure.  For  it  is  more  probable  that  all  the  particles 
of  the  air  should  have  a  faintly  bluish  cast,  but  so 
very  faint  as  to  be  imperceptible  till  presented  in  a 
prodigious  mass,  such  as  the  whole  extent  of  the 
atmosphere,  than  that  this  colour  is  to  be  ascribed 
to  vapours  floating  in  the  air,  but  which  do  not  ap- 
pertain to  it. 

7.  In  fact,  the  purer  the  air  is,  and  the  more  purged 
from  exhalation,  the  brighter  is  the  lustre  of  heaven's 
azure  ;  which  is  a  sufficient  proof  that  we  must 
look  for  the  reason  of  it  in  the  nature  of  the  proper 
particles  of  the  air.  Extraneous  substances  min- 
gling with  it,  such  as  exhalations,  become,  on  the 
contrary,  injurious  to  that  beautiful  azure,  and  serve 
to  diminish  its  lustre.  When  the  air  is  overloaded 
with  such  vapours,  they  produce  fogs  near  the  sur- 
face, and  entirely  conceal  from  us  the  azure  appear- 
ance ;  when  they  are  more  elevated,  as  is  frequently 
the  case,  they  form  clouds,  which  frequently  cover 
the  whole  face  of  the  sky,  and  present  a  very  dif- 
ferent colour  from  that  of  this  azure  of  the  pure  air. 
This,  then,  is  a  new  quality  of  air,  different  from 
those  formerly  explained — subtilty,  fluidity,  and 
elasticity ;  namely,  the  minute  particles  of  air  are  in 
their  nature  bluish. 

llth  May,  1762. 


LETTER  CXVII. 

What  the  Appearance  would  be  were  the  Air  perfectly 
transparent. 

INDEPENDENT  of  the  beautiful  spectacle  of  the  azure 
heavens  procured  for  us  by  this  colour  of  the  cir- 
cumambient air,  we  should  be  miserable  in  the 
extreme  were  it  perfectly  transparent,  and  divested 


OF    TRANSPARENT  AIR.  411 

of  those  bluish  particles  ;  and  we  have  here  a  new 
reason  for  adoring  the  infinite  wisdom  and  goodness 
of  the  CREATOR. 

That  you  may  have  full  conviction  of  the  truth  of 
my  assertion,  let  us  suppose  the  air  to  be  quite  trans- 
parent, and  similar  to  the  ether,  which,  we  know, 
transmits  all  the  rays  of  the  stars,  without  inter- 
cepting so  much  as  one,  and  contains  no  particles 
themselves  illuminated  by  rays,  for  such  a  particle 
could  not  be  so  without  intercepting  some  of  the 
rays  which  fell  upon  it.  If  the  air  were  in  this  state, 
the  rays  of  the  sun  would  pass  freely  through  it, 
without  the  retransmission  of  any  light  to  the  eye  : 
we  should  receive,  then,  those  rays  only  which  came 
to  us  immediately  from  the  sun.  The  whole  heavens, 
except  the  spot  occupied  by  the  sun,  would  appear, 
therefore,  completely  dark  ;  and  instead  of  this  bril- 
liant blue,  we  should  discover  nothing  on  looking 
upward  but  the  deepest  black  and  the  most  profound 
night.  pig.  208. 

Fig.  208  represents  the  sun  M 
E  F,  and  the  point  O  is  the  eye 
of  a  spectator,  which  would  re- 
ceive from  above  no  other  rays 
but  those  of  the  sun,  so  that 
all  illumination  would  be  lim-  0 
ited  to  the  space  of  the  small  angle  E  0  P.  On  di- 
recting the  eye  towards  any  other  quarter  of  the 
heavens,  say  towards  M,  not  a  single  ray  would  be 
emitted  from  it,  and  the  appearance  would  be  the 
same  as  if  we  looked  into  total  darkness  ;  now  every 
place  which  transmits  no  ray  of  light  is  black.  But 
here  the  stars  must  be  excepted,  which  are  spread 
over  the  whole  face  of  the  heavens ;  for  on  directing 
the  eye  towards  M,  nothing  need  prevent  the  rays  of 
the  stars  which  may  be  in  that  quarter  from  entering 
into  it ;  nay,  they  would  have  even  still  more  force, 
as  they  could  suffer  no  diminution  of  lustre  from  the 
atmosphere,  such  as  I  am  now  supposing  it.  All  the 


412  OF    TRANSPARENT    AIR. 

stars,  therefore,  would  be  visible  at  noon-day,  as  in 
the  darkest  night ;  but  it  must  be  considered  that  this 
whole  ray  would  be  reduced  to  the  space  of  the  little 
angle  EOF;  all  the  rest  of  the  heavens  would  be 
black  as  night. 

At  the  same  time,  stars  near  the  sun  would  be 
invisible ;  and  we  should  not  be  able  to  see,  for  ex- 
ample, the  star  N.  for  on  looking  to  it  the  eye  would 
likewise  receive  the  rays  of  the  sun,  with  which  it 
must  be  struck  so  forcibly  that  the  feeble  light  of  the 
star  could  not  excite  any  sensation.  I  say  nothing 
of  the  impossibility  of  keeping  the  eye  open  in  at- 
tempting to  look  towards  N.  This  is  too  obvious 
not  to  be  understood. 

But  on  opposing  to  the  sun  an  opaque  body,  which 
shall  intercept  his  rays,  you  could  not  fail  to  see  the 
star  N,  however  near  it  might  be  to  the  sun.  It  is 
easy  to  comprehend  in  what  a  dismal  state  we  should 
then  be.  This  proximity  of  lustre  insupportable 
and  darkness  the  most  profound  must  destroy  the 
organs  of  vision,  and  quickly  reduce  us  to  total  blind- 
ness. Of  this  some  judgment  may  be  formed  from 
the  inconvenience  we  feel  on  passing  suddenly  from 
darkness  into  light. 

Now  this  dreadful  inconvenience  is  completely 
remedied  by  the  nature  of  the  air,  from  its  contain- 
ing particles  opaque  to  a  very  small  degree,  and  sus- 
ceptible of  illumination.  Accordingly,  the  moment 
the  sun  is  above  the  horizon,  nay,  somewhat  earlier, 
the  whole  atmosphere  becomes  illuminated  with 
his  rays,  and  we  are  presented  with  that  beautiful 
azure  which  I  have  described,  so  that  our  eyes,  which- 
ever way  directed,  receive  a  great  quantity  of  rays 
generated  in  the  same  particles.  Thus,  on  looking 
towards  M,  Fig.  208,  p.  411,  we  perceive  a  great  de- 
gree of  light  produced  by  this  brilliant  azure  of  the 
heavens. 

This  very  illumination  of  the  atmosphere  prevents 
our  seeing  the  stars  by  day :  the  reason  of  this  is  ob- 


OF    TRANSPARENT    AIR.  413 

vious.  It  far  exceeds  that  of  the  stars,  and  the  greater 
light  always  makes  the  lesser  to  disappear ;  and  the 
nerves  of  the  retina  at  the  bottom  of  the  eye,  being 
already  struck  by  a  very  strong  light,  are  no  longer 
sensible  to  the  impression  made  by  the  feebler  light 
of  the  stars. 

You  will  please  to  recollect  that  the  light  of  the 
full  moon  is  upwards  of  200,000  times  more  faint 
than  that  of  the  sun ;  and  this  will  convince  you 
that  the  light  proceeding  from  the  stars  is  a  mere 
nothing  in  comparison  with  the  light  of  the  sun. 
But  the  illumination  of  the  heavens  in  the  day-time, 
even  though  the  sun  should  be  overclouded,  is  so 
great  as  many  thousand  times  to  exceed  the  light  of 
the  full  moon. 

You  must  have  frequently  perceived  that  in  the 
night  when  the  moon  is  full,  the  stars  appear  much 
less  brilliant,  and  that  those  only  of  superior  magni- 
tude are  visible,  especially  in  the  moon's  vicinity ;  a 
sufficient  proof  that  the  stronger  light  always  absorbs 
the  feebler. 

It  is  then  an  unspeakable  benefit,  that  our  atmo- 
sphere begins  to  be  illuminated  by  the  sun  even 
before  he  rises,  as  we  are  thereby  prepared  to  bear 
the  vivacity  of  his  rays,  which  would  otherwise  be 
insupportable,  that  is,  if  the  transition  from  night  to 
day  were  instantaneous.  The  season  during  which 
the  atmosphere  is  gradually  illuminated  before  sun- 
rising,  and  continues  to  be  illuminated  after  he  sets, 
is  denominated  twilight.  This  subject,  from  its  im- 
portance, merits  a  particular  explanation,  which  I 
propose  to  attempt  in  my  next  Letter  ;  and  thus  one 
article  in  physics  naturally  runs  into  another. 
15th  May,  1762. 

Mm  2 


414  REFRACTION    OF   LIGHT. 


LETTER  CXVIII. 

Refraction  of  Rays  of  Light  in  the  Atmosphere,  and 
its  Effects.  Of  the  Twilight.  Of  the  apparent  rising 
and  setting  of  the  Heavenly  Bodies. 

IN  order  to  explain  the  cause  of  the  twilight,  or 
that  illumination  of  the  heavens  which  precedes 
the  rising  of  the  sun,  and  continues  some  time  after 
he  is  set,  I  must  refer  you  to  what  has  been  already 
demonstrated  respecting  the  horizon  and  the  atmo- 
sphere. 

Let  the  circle  A  O  B  D,  Fig.  209,  represent  the 
earth,  and  the  dotted  circle  j^  399. 

a  o  b  d  the  atmosphere;  let  ^     a. ......<?.... R  ! 

a  point  O  be  assumed  on  the 
surface  of  the  earth,  through 
which  draw  the  straight  line 
H  O  R  I,  touching  the  earth 
at  0,  and  this  line  H  I  will 
represent  the  horizon,  which 
separates  that  part  of  the 
heavens  which  is  visible  to  us  from  that  which  is 
not.  As  soon  as  the  sun  has  reached  this  line,  he 
appears  in  the  horizon,  both  at  rising  and  setting, 
and  the  whole  atmosphere  is  then  completely  illu- 
minated. But  let  us  suppose  the  sun  before  his 
rising  to  be  still  under  the  horizontal  line  at  S ;  from 
which  the  ray  S  T  R,  grazing  the  earth  at  T,  may 
reach  the  point  of  the  atmosphere  situated  in  our 
horizon ;  the  opaque  particles  which  are  there  will 
already  be  illuminated  by  that  ray,  and  consequently 
have  become  visible.  Accordingly,  some  time  be- 
fore the  rising  of  the  sun,  the  atmosphere  hoR  over 
our  horizon  begins  to  be  illuminated  at  R ;  and  in 
proportion  as  the  sun  approaches  the  horizon  a 


REFRACTION   OF   LIGHT.  415 

greater  part  of  it  will  be  illuminated,  till  it  becomes 
at  length  completely  luminous. 

This  reflection  leads  me  forward  to  another  phe- 
nomenon equally  interesting,  and  very  intimately 
connected  with  it,  namely,  that  the  atmosphere  dis- 
covers to  us  the  body  of  the  sun  and  of  the  other 
stars  some  time  before  they  get  above  the  horizon, 
and  some  time  after  they  have  fallen  below,  by 
means  of  the  refraction  which  rays  of  light  undergo 
on  passing  from  the  pure  ether  into  the  grosser  air 
which  constitutes  our  atmosphere ;  of  this  I  proceed 
to  give  you  the  demonstration. 

1.  Rays  of  light  do  not  continue  to  proceed  for- 
ward in  a  straight  line  any  longer  than  they  move 
through  a  transparent  medium  of  the  same  nature. 
As  soon  as  they  pass  from  one  medium  to  another, 
they  are  diverted  from  their  rectilinear  direction— 
their  path  is,  as  it  were,  broken  off;  and  this  is  what 
we  call  refraction,  which  1  formerly  explained  at 
considerable  length,  and  demonstrated  that  rays,  on 
passing  from  air  into  glass,  and  reciprocally,  are 
thus  broken  or  refracted. 

2.  Now  air  being  a  different  medium  from  ether, 
when  a  ray  of  light  passes  from  ether  into  air  it 
must  of  necessity  undergo  some  refraction. 

Thus,  the  arch  of  the  circle  A  M  B,  Fig.  210,  ter- 
minating our  upper  atmosphere,  if  a        pi-  210 
ray  of  light  M  S,  from  the  ether,  falls 
upon  it  at  M,  it  will  nofc  proceed 
straight  forward  in  the  same  direc- 
tion M  N,  but  will  assume,  on  en- 
tering into  the  air,  the  direction 
M  R,  somewhat  different  from  M  N ;  AN 
and  the  angle  N  M  R  is  denomi- 
nated the  angle  of  refraction,  or  simply  the  refrac- 
tion. 

3.  I  have  already  remarked,  that  the  refraction  is 
greater  in  proportion  as  the  ray  S  M  falls  more  ob- 
liquely on  the  surface  of  the  atmosphere,  or  as  the 


416  REFRACTION    OF    LIGHT. 

angle  B  M  S  is  smaller  or  more  acute.     I 
ray  S  M  falls  perpendicularly  on  the  surface  of  trie 
atmosphere,  that  is,  if  the  angle  B  M  S  is  a  right 
angle,  no  refraction  will  take  place,  but  the  ray  will 
pursue  its  progress  in  the  same  straight  line.    This 
rule  is  universally  applicable  to  every  kind  of  refrac- 
tion, whatever  may  be  the  nature  of  the  two  media 
through  which  the  rays  travel. 
4.  Let  the  arch  of  the  circle  A  O  B,  Fig.  211, 

Fig.  211. 


represent  the  surface  of  the  earth,  and  the  arch 
E  M  F  terminate  the  atmosphere.  If  you  draw  at 
O  the  line  0  M  V,  touching  the  surface  of  the  earth 
at  0,  it  will  be  horizontal.  And  if  the  sun  is  still 
under  the  horizon  at  S,  so  as  to  be  still  invisible 
(for  no  one  of  his  rays  can  yet  reach  us  in  a  straight 
line),  the  ray  S  M  being  continued  in  a  straight  line 
would  pass  over  us  to  N ;  but  as  it  falls  on  the  at- 
mosphere at  M,  and  in  a  very  oblique  direction,  the 
angle  F  M  S  being  very  acute,  it  will  thence  undergo 
a  very  considerable  refraction ;  and  instead  of  pro- 
ceeding forward  to  N,  would  assume  the  direction 
M  O,  so  that  the  sun  would  be  actually  visible  to  a 
person  at  O,  though  still  considerably  below  the 
horizon  at  S ;  or,  which  is  the  same  thing,  below  the 
horizontal  line  O  M  V. 

5.  However,  as  the  ray  M  0,  which  meets  the 
eye,  is  horizontal,  we  assign  that  direction  to  the 
sun  himself,  and  imagine  him  to  be  actually  at  V, 
that  is,  in  the  horizon,  though  he  is  still  below  it. 


ELEVATION  OF  THE  STARS.        417 

And,  reciprocally,  as  often  as  we  see  the  sun,  or 
any  star,  in  the  horizon,  we  are  assured  they  are 
still  below  it,  according  to  the  angle  S  M  V,  which 
astronomers  have  observed  to  be  about  half  a  degree, 
or,  more  exactly,  32  minutes. 

6.  In  the  morning,  then,  we  see  the  sun  before  he 
has  reached  our  horizon,  that  is,  while  he  is  yet  an 
angle  of  32  minutes  below  it ;  and  in  the  evening  a 
considerable  time  after  he  is  really  set,  as  we  see 
him  till  he  has  descended  an  angle  of  32  minutes. 
We  call  that  the  true  rising  and  setting  of  the  sun 
when  he  is  actually  in  the  horizon ;  and  the  com- 
mencement of  his  appearance  in  the  morning  and 
disappearing  at  night  we  denominate  the  apparent 
rising  and  setting. 

7.  This  refraction  of  the  atmosphere,  which  ren- 
ders the  apparent  rising  and  setting  of  the  sun  both 
earlier  and  later  than  the  real,  procures  for  us  the 
benefit  of  a  much  longer  day  than  we  should  enjoy 
did  not  the  atmosphere  produce  this  effect.     Such 
is  the  explanation  of  a  very  important  phenomenon 
in  nature. 

18th  May,  1762. 

LETTER  CXIX. 

The  Stars  appear  at  a  greater  Elevation  than  they  are. 
Table  of  Refractions. 

You  have  now,  no  doubt,  a  clear  idea  of  this  sin- 
gular effect  of  our  atmosphere,  by  which  the  sun 
and  the  other  heavenly  bodies  are  rendered  visible 
in  the  horizon,  though  considerably  below  it, 
whereas  they  would  be  invisible  but  for  the  refrac- 
tion. For  the  same  reason  the  sun,  and  all  the 
heavenly  bodies  always  appear  at  a  greater  eleva- 
tion above  the  horizon  than  they  really  are.  It  is 
necessary,  therefore,  carefully  to  distinguish  the 


418 


ELEVATION    OF    THE    STARS. 


apparent  elevation  of  a  star  from  what  it  would  be 
were|jthere  no  atmosphere.     I  shall  endeavour  to 
set  this  in  the  clearest  light  possible. 
1.  Let  the  arch  A  O  B,  Pig.  212,  be  part  of  the 

Fig.  212. 


A  B 

surface  of  the  earth,  and  O  the  spot  where  we  are, 
through  which  draw  the  straight  line  H  0  R,  touch- 
ing the  surface,  and  this  line  H  O  R  will  represent 
the  true  horizon.  From  O  let  there  be  drawn  per- 
pendicularly the  straight  line  0  Z,  which  is  the  same 
thing  as  suspending  a  given  weight  by  a  cord.  This 
line  is  said  to  be  vertical,  and  the  point  Z  of  the 
heavens,  in  which  it  terminates,  is  called  the  zenith. 
This  line,  0  Z,  then,  is  perpendicular  to  the  horizon- 
tal line  H  0  R,  so  that  one  being  known,  the  other 
must  be  known  likewise. 

2.  This  being  laid  down,  let  there  be  a  star  at  S, 
Fig.  213 :  were  there  no  atmo- 
sphere, the  ray  S  M  0  would  Fig.  213. 
proceed  in  a  straight  line  to  the 
eye  at  0,  and  we  should  see  it 
in  the  same  direction  0  M  S,  HL 
where  it   would  actually  be — 
that  is,  we  should  see  it  in  its     ^ 
true  place.    Let  us  then  mea- 


ELEVATION  OF  THE  STARS.        419 

sure  the  angle  S  0  R,  formed  by  the  ray  S  0  with 
the  horizon  O  R,  and  this  angle  is  named  the  height 
of  the  star,  or  its  elevation  above  the  horizon.  We 
measure  also  the  angle  S  0  Z,  formed  by  the  ray  S  O 
with  the  vertical  line  0  Z  terminating  in  the  zenith : 
and  as  the  angle  Z  0  R  is  a  right  angle,  or  90  de- 
grees, we  have  only  to  subtract  the  angle  S  O  Z 
from  90  degrees  to  have  the  angle  S  0  R,  which 
gives  the  true  elevation  of  the  star. 

3.  But  let  us  now  attend  to  the  atmosphere,  which 
I  suppose  terminated  by  the   arch  II  D  N  M  R, 
Fig.  212,  p.  418,  and  I  remark,  first,  that  the  pre- 
ceding ray  S  M  of  the  star  S,  on  entering  into  M  in 
the  atmosphere,  does  not  proceed  directly  forward 
to  the  eye  at  0,  but,  from  the  refraction,  will  assume 
another  direction,  as  M  P,  and  consequently  will  not 
meet  the  eye  at  O :  so  that  if  this  star  sent  down 
to  the  earth  only  that  ray  S   M,   to  a  person  at 
O  it  would  be  absolutely  invisible.     But  it  must 
be  considered  that  every  luminous  point  emits  its 
rays  in  all  directions,  and  that  all  space  is  filled  with 
them. 

4.  There  will  be,  then,  among  others,  some  ray, 
as  S  N,  which  is  broken  or  refracted  on  entering 
the  atmosphere  at  N ;  so  that  its  continuation  N  O 
shall  pass  precisely  to  an  eye  at  O.     The  refracted 
ray  N  0  is  not,  therefore,  in  a  straight  line  with  the 
ray  S  M ;  and  if  N  O  be  produced  forward  to  s,  the 
continuation  N  s  will  form  an  angle  with  the  ray 
N  S,  namely,  the  angle  S  N  5,  which  is  what  we 
call  the  refraction,  and  which  is  greater  in  propor- 
tion as  the  angle  S  N  R,  under  which  the  ray  S  N 
enters  into  the  atmosphere,  is  more  acute,  as  was 
demonstrated  in  the  preceding  Letter. 

5.  It  is  the  ray  N  O,  consequently,  which  paints  in 
the  eye  the  image  of  the  star  S,  and  which  renders 
it  visible :  and  as  this  ray  comes  in  the  direction 
N  0,  as  if  the  star  were  in  it,  we  imagine  the  star 
likewise  to  be  situated  in  the  direction  N  0,  or  in 


420        ELEVATION  OF  THE  STARS. 

th^t  line  continued  somewhere  at  s.  This  point  s 
being  different  from  the  real  place  of  the  star  S, 
we  call  s  the  apparent  place  of  the  star,  which 
must  be  carefully  distinguished  from  its  place  S, 
where  the  star  would  be  seen  were  there  no  atmo- 
sphere. 

6.  Since,  then,  the  star  is  seen  by  the  ray  N  0, 
the  angle  NOR,  which  this  ray  N  O  makes  with 
the  horizon,  is  the  apparent  altitude  of  the  star ;  and 
when  by  a  proper  instrument  we  measure  the  angle 
NOR,  we  are  said  to  have  found  the  apparent  alti- 
tude of  the  star ;  the  real  altitude  being,  as  we  have 
shown,  the  angle  R  O  S. 

7.  Hence  it  is  evident,  that  the  apparent  altitude 
R  0  N  is  greater  than  the  real  altitude  R  O  M,  so  that 
the  stars  appear  to  us  at  a  greater  elevation  above 
the  horizon  than  they  really  are ;  for  the  same  rea- 
son they  appear  already  in  the  horizon  while  they 
are  still  below  it.     Now,  the  excess  of  the  apparent 
altitude  above  the  true  is  thfc  angle  M  ON,  which 
does  not  differ  from  the  angle  S  N  s,  and  which  we 
call  the  refraction.     For,  though  the  angle  S  N  s,  as 
being  the  external  angle  to  the  triangle  S  N  O,  is 
equal  to  the  two  internal  and  opposite  angles  taken 
together,  namely,  SON  and  N  S  O,  we  may  con- 
sider, on  account  of  the  immense  distance  of  the 
stars,  the  lines  O  S  and  N  S  as  parallel,  and  conse- 
quently the  angle  O  S  N  vanishes;   so  that  the 
angle  S  O  N  is  nearly  equal  to. the  angle  of  refrac- 
tion S  N  5. 

8.  Having  found,  then,  the  apparent  altitude  of  a 
star,  you  must  subtract  from  it  the  refraction,  in 
order  to  have  the  real  altitude,  which  there  is  no 
other  method  of  discovering.      For  this  purpose, 
astronomers  have  been  at  much  pains  to  ascertain 
the  refraction  to  be  subtracted  from  each  apparent 
altitude,  that  is,  to  determine  how  much  must  be 
deducted  in  order  to  reduce  the  apparent  to  the  real 
altitude. 


CONCLUSION.  421 

9.  From  a  long  series  of  observations,  they  have 
been  at  length  enabled  to  construct  a  table,  called 
the  table  of  refraction,  in  which  is  marked  for  every 
apparent  altitude  the  refraction  or  angle  to  be  sub- 
tracted.    Thus,  when  the  apparent  altitude  is  no- 
thing, that  is,  when  the  star  appears  in  the  horizon, 
the  refraction  is  32  minutes  ;  the  star  is  accordingly 
an  angle  of  actually  32  minutes  below  the  horizon. 
But  if  the  star  has  acquired  any  degree  of  elevation, 
be  it  ever  so  inconsiderable,  the  refraction  becomes 
much  less.     At  the  altitude  of  15  degrees  it  is  no 
more  than  four  minutes ;  at  the  altitude  of  40  de- 
grees it  is  only  one  minute ;   and  as  the  altitude 
increases,  the  refraction  always  becomes  less,  till  at 
length  it  entirely  disappears  at  the  altitude  of  90 
degrees. 

10.  This  is  the  case  when  a  star  is  seen  in  the 
very  zenith ;  for  its  elevation  is  then  90  degrees,  and 
the  real  and  apparent  altitude  is  the  same :  and  we 
are  fully  assured  that  a  star  seen  in  the  zenith  is 
actually  there,  and  that  the  refraction  of  the  atmo- 
sphere does  not  change  its  place,  as  at  every  other 
degree  of  altitude. 


THE   END, 


VOL.  II.— N  n 


GLOSSARY 

OF 

FOREIGN  AND  SCIENTIFIC  TERMS. 

FEOM  THE   LONDON   EDITION,   REVISED. 


A. 

ABERRATION,  in  astronomy,  an  apparent  motion  in  the  celestial  bodies, 
occasioned  by  the  progressive  motion  of  light,  and  the  earth's  annual 
motion.  Latin. 

Abstraction,  in  metaphysics,  that  operation  of  the  mind  which  pursues  a 
general  idea  without  attending  to  the  particulars  of  which  it  is  made 
up.  Thus,  man, tree,  are  abstract  ideas,  and  may  be  pursued  with- 
out descending  to  any  one  individual  person  or  plant  included  in  the 
general  term.  Accordingly,  all  qu  alities,  such  as  whiteness,  cruelty, 
generosity,  are  abstract  ideas.  Latin. 

Accord,  in  music,  the  same  with  concord,  the  relation  of  two  sounds 
which  are  always  agreeable  to  the  ear,  whether  emitted  at  once  or 
in  succession.  Latin. 

Achromatic  Glasses,  in  optics,  are  those  which  bring  diffused  rays  of 
light  to  a  focus,  and  form  an  image  free  from  any  unnatural  colour. 
The  word  is  of  Greek  extraction,  and  signifies  colourless. 

Aeriform,  having  the  form  or  consistency  of  air.    Latin. 

Aerostation,  the  art  of  ascending  into  the  atmosphere  by  means  of  a 
balloon  filled  with  air  or  gas  lighter  than  that  of  the  atmosphere. 
Latin. 

Affirmative  proposition,  in  logic,  a  proposition  which  asserts  or  affirms ; 
as,  Man  is  mortal.  Latin. 

Air-pump,  a  machine  for  making  experiments  on  air,  chiefly  by  exhaust- 
ing close  vessels  of  that  fluid. 

Algebra,  the  science  of  universal  arithmetic ;  the  general  process  of 
which  is,  by  comparing  supposed  and  unknown  numbers  or  quan- 
tities with  such  as  are  known,  to  reduce  supposition  to  certainty. 
Arabic. 

Alkali,  in  chymistry,  a  substance  which  turns  vegetable  blues  to  green, 
and  unites  with  oils  and  forms  soap,  and  with  acids  and  forms  salts. 
Arabic, 

Altitude,  in  astronomy,  the  height  of  a  heavenly  body  above  the  horizon. 
Latin. 

Amalgamate,  to  incorporate  mercury  or  quicksilver  with  other  metals , 
sometimes  used  to  denote,  in  general,  the  mixture  and  consolidation 
of  several  substances,  so  as  to  make  them  appear  one.  Greek. 


424  GLOSSARY. 

Analogous,  having  resemblance  or  agreement,    Greek. 

Analysis,  resolution  into  first  principles,  whether  in  grammar,  logic, 
mathematics,  or  chymistry.  In  grammar,  an  analysis  of  a  sentence 
is  an  indication  of  the  various  parts  of  speech  of  which  it  \a  com- 
posed, and  the  grammatical  rules  according  to  which  they  are  ar- 
ranged. A  ckymical  analysis  is  the  decomposition  of  a  body  for  the 
purpose  of  ascertaining  its  elementary  or  constituent  parts.  Greek. 

Anathema,  and  its  compounds,  something  set  apart  to  a  sacred  use; — 
generally  used  in  an  ungracious  sense ;  devoted  to  destruction,  ac- 
cursed. Greek. 

Anatomy,  the  science  which  treats  of  the  structure  of  the  body,  and 
the  art  of  dissecting  and  reasoning  upon  it.  Greek. 

Angle,  the  opening  of  two  lines  which  meet  in  a  point,  so  as  not  to  form 
of  both  one  straight  line.  Latin. 

Antecedent,  in  logic,  the  former  of  two  propositions  in  a  species  of  rea- 
soning, which,  without  the  intervention  of  any  middle  proposition, 
leads  directly  to  a  fair  conclusion  ;  and  this  conclusion  is  termed  the 
Consequent,  Thus— 1  reflect ;  therefore  I  exist.  "  I  reflect"  is  the 
an'ecedent,  "  therefore  I  exist"  is  the  consequent.  Latin. 

Antipodes,  the  inhabitants  of  the  globe  diametrically  opposite  to  us,  and 
whose  feet  point  exactly  to  our  feet.  Greek. 

Aperture,  opening.    Latin. 

Approximation,  a  coming  nearer  to.  In  astronomy,  the  gradual  ap- 
proach of  two  celestial  bodies  towards  each  other.  In  arithmetic, 
a  nearer  approach  to  a  number  or  root  sought,  without  the  possi- 
bility of  arriving  at  it  exactly.  Latin. 

Aqueduct,  that  which  conveys  or  conducts  water.  A  pipe,  a  canal 
Latin. 

Aqueous,  watery,  consisting  of  water.    Latin. 

Arithmetic,  the  science  of  numbers.    Greek. 

Astronomy,  the  science  of  the  heavenly  bodies.    Greek. 

Astrology,  the  pretended  science  of  predicting  future  events  by  means 
of  the  planets.  Greek. 

Atmosphere,  the  body  of  air  which  surrounds  the  globe  on  all  sides. 
Greek. 

Axis,  in  geography,  an  imaginary  straight  line  passing  through  the 
centre  of  the  earth  from  pole  to  pole,  round  which  the  globe  revolves 
once  every  twenty-four  hours.  Latin. 

B. 

Barometer,  an  instrument  of  glass  filled  with  mercury,  which  indicates 
the  pressure  of  the  air,  and  which  is  in  general  use  as  an  index  of 
the  weather.  The  word  is  Greek,  and  signifies  weight-measurer. 

Bisect,  to  cut  into  two  equal  parts     Latin. 

Bituminous,  like  to  or  consisting  of  bitumen, — a  fat,  clammy,  easily- 
inflammable  juicef  impregnating  coal,  or  scummed  off  lakes.  Latin. 

Bomb,  a  hollow  cast-iron  globe,  to  be  thrown  from  a  species  of  great 
gun  called  mortar,  and  intended  to  burst  by  the  force  of  gunpowder 
at  the  moment  of  falling,  and  to  scatter  destruction  all  around. 
The  term  is  in  this  work  employed  to  explain  the  path  of  all  bodies 
forcibly  thrown  through  the  air,  and  the  effect  of  gravity  in  bringing 
all  heavy  moving  bodies  to  the  ground.  Latin. 

Botany,  the  science  of  plants,  or  that  part  of  natural  history  which 
has  the  vegetable  world  for  its  object.  Greek. 


GLOSSARY.  425 

C. 

Camera  Obscura,  an  apartment  darkened,  all  but  a  small  circular  open 
ing,  to  which  a  double-convex  glass  is  fitted,  and  by  which  ex- 
ternal objects  are  represented  in  their  natural  colours,  motions, 
and  proportions,  on  a  white  skreeri  within  the  apartment.  Latin. 

Cataract,  a  body  of  water  precipitated  from  a  great  height.     Greek. 

Catoptrics,  that  branch  of  the  science  of  vision  which  relates  to  reflected 
light.  The  reflective  properties  of  all  bodies  through  which  we  can- 
not see,  but  which  throw  back  the  light,  belong  to  catoptrics,  such 
as  mirrors  of  every  kind.  The  word  is  Greek,  and  signifies  back- 
ward vision. 

Cavity,  a  hollow.    Latin. 

Causa  sufficiens,  sufficient  or  satisfying  cause  or  reason,  a  jargon  em- 
ployed by  certain  metaphysicians  of  the  last  age,  who  attempted  to 
check  all  rational  experimental  inquiry  by  calling  continually  for  the 
causa  sufficiens,  or  adequate  cause,  of  every  fact  that  occurred ; 
while  they  were  bewildering  themselves,  and  attempting  to  bewilder 
mankind,  in  a  philosophical  maze  useless,  reasonless,  and  therefore 
unsatisfactory. 

Centre,  a  point  within  a  circle  or  sphere  equally  distant  from  every  part 
of  the  circumference  or  surface.  Latin. 

Chart ,  a  delineation  on  paper  of  part  of  the  land  or  of  the  sea,  or  both. 
Latin. 

Chimera,  a  vain  and  wild  imagination.    Latin. 

Choral  Music,  a  sacred  band  composed  of  voices  and  instruments. 
Latin. 

Chromatic,  in  optics,  relating  to  colour  :  in  music,  to  a  certain  series  of 
sounds.  Greek. 

Chymistry,  the  science  which  treats  of  the  composition  of  matter  in  its 
various  conditions,  of  the  nature  of  its  elementary  principles,  and 
of  the  intimate  affinities  of  simple  and  compound  bodies. 

Circle,  a  round  figure  having  the  essential  property  that  every  point  of  its 
surrounding  line,  called  the  circumference,  shall  be  equally  distant 
from  its  middle  point,  called  the  centre.  Latin. 

Circumambient,  encompassing,  surrounding ;  applied  particularly  to  air 
and  water.  Latin. 

Cohesion,  that  species  of  attraction  which  unites  the  particles  of  bodies, 
and  produces  solidity  in  its  various  degrees.  Latin. 

Collision,  the  clashing  of  one  body  against  another.     Latin. 

Comet,  a  body  with  a  luminous  train,  like  flowing  hair,  averted  from  the 
sun;  of  uncertain  appearance  and  reappearance,  but  undoubtedly 
forming  part  of  our  solar  system.  Greek. 

Complex,  made  up  of  various  qualities  or  ingredients.  A  beautiful, 
wise,  and  good  woman,  is  a  complex  idea,  containing  three  distinct 
ideas — beauty,  wisdom,  goodness :  it  might  be  rendered  still  more 
complex  by  the  addition  of  highborn,  rich,  religious. 

Compression,  the  act  of  reducing  to  a  smaller  space  by  pressure. 

Concave,  the  hollowed  surface  of  a  curvilinear  body.     Latin. 

Concussion,  mutual  shock,  by  the  violent  meeting  of  two  bodies.    Latin. 

Condensation,  the  act  of  forcing  matter  into  a  smaller  space.    Latin. 

Cuiig-latiiin,  the  reduction  of  a  fluid  to  a  solid  substance,  as  water  to  ice, 
by  cold.  Latin. 

Concentric  Circles,  one  within  another,  having  a  common  centre. 
Latin. 

Nn2 


426  GLOSSARY. 

Conicfl,  having  the  form  of  a  cone,  which  is  a  figure  produced  by  turn- 
ing round  a  right-angled  triangle  about  its  perpendicular  side ;  a 
common  candle-extinguisher  conveys  the  idea  of  it.  Greek. 

Consequent.  See  Antecedent.  The  two  terms  are  what  is  called  cor- 
relative ;  in  other  words,  the  one  cannot  be  understood  but  by  re- 
ferring to  the  other. 

Consonance,  in  music,  the  agreement  of  two  sounds  emitted  at  the  same 
time.  Latin. 

Constituent,  contributing  to  make  up  or  compose.  Thus  the  constituent 
parts  of  gunpowder  are  saltpetre,  sulphur,  and  charcoal.  Latin. 

Continuity,  uninterrupted  connexion ;  the  unviolated  union  of  the  parts 
of  an  animal  body.  Latin. 

Contexture,  an  interweaving.    Latin. 

Contour,  the  extreme  bounding  line  of  any  object.  Children  delineate 
the  contours  of  each  other's  faces  by  tracing  with  a  pencil  the  line 
described  on  the  wall  when  the  face  is  placed  between  a  light  and 
the  wall.  French. 

Convergent,  gradually  approaching.  Placed  at  the  extremity  of  an 
avenue  of  two  rows  of  trees,  planted  in  straight  lines,  equally  distant 
throughout,  you  perceive  them  apparently  approaching,  and  at  length 
almost  meeting ;  they  are  apparently  convergent. 

Co-nvex,  the  prominent  or  swelling  surface  of  a  curvilinear  body.    Latin. 

Cornea,  the  transparent  portion  of  the  external  coat  of  the  eye.    Latin. 

Corvorea',  belonging  to  body.    Latin. 

Corpus  Callosum,  in  metaphysics  and  anatomy,  the  part  of  the  human 
brain  where  the  soul  is  supposed  to  reside.  Latin,  but  of  ludicrous 
derivation. 

Corpuscle,  a  small  or  minute  body.    Latin. 

Couching,  an  operation  in  surgery,  that  consists  in  removing  the  opaque 
lens  out  of  the  axis  of  vision,  by  means  of  a  needle  constructed  for 
the  purpose. 

Crucible,  a  pot  which  can  stand  fire,  employed  in  melting  and  refining 
metals.  Low  Latin. 

Crystalline,  the  solid,  transparent,  internal  humour  of  the  eye.  It  is  a 
double-convex  lens,  situated  immediately  behind  the  pupil.  Its  oc- 
casional opacity  produces  the  disease  called  cataract.  Greek. 

Cube,  and  its  compounds,  a  figure  square  and  rectangular  in  all  its  di- 
mensions and  situations.  A  common  die  conveys  the  idea  of  it. 
A  cubical  room  of  twenty  feet  is  a  room  twenty  feet  long,  twenty 
feet  broad,  and  twenty  feet  high,  and  all  in  straight  lines,  and  at 
right  angles.  Greek. 

Curve,  a  bending  line.    Latin. 

Cylinder,  a  figure  formed  by  turning  a  parallelogram  round  one  of  its 
sides  as  an  axis.  The  barrel  of  a  hand-organ  is  a  cylinder.  The 
word  is  derived  from  a  Greek  verb  which  signifies  to  whirl  round. 

D. 

Decompose,  to  separate  things  compounded.  Thus,  in  printing,  to  com- 
pose is  to  arrange  the  types  in  a  frame,  in  the  order  of  words  and 
sentences  ;  and  to  decompose  is  to  take  the  frame  10  pieces.  Latin. 

Degree,  in  geography,  the  three  hundred  and  sixtieth  part  of  the  circum- 
ference of  the  globe.  It  contains  about  sixty-nine  English  miles. 
French. 

Density,  comparative  solidity.    Latin. 


GLOSSARY.  427 

Dephlogistic,  deprived  of  flery,  inflammable  qualities.    Greek. 

Detonation,  the  thunder-like  noise  produced  by  explosions.     Latin. 

Diagram,  a  figure  delineated  for  the  purpose  of  demonstration  and  ex- 
planation. Greek. 

Diameter,  a  straight  line  drawn  through  the  centre  of  a  circle  or  globe. 
Greek. 

Diaphanous  body,  that  which  easily  transmits  the  light,  as  glass. 
Greek. 

Diaphragm,  in  optical  instruments,  a  circular  piece  of  pasteboard,  or 
other  non-transparent  substance,  applied  to  the  object-glass  to  ex- 
clude part  of  the  rays  of  light.  Greek. 

Diatonic,  an  epithet  given  to  the  common  music,  as  it  proceeds  by  tones 
both  ascending  and  descending.  Greek. 

Dilate,  to  expand,  to  spread  over  greater  space.    Latin. 

Dimension,  measure.     Latin. 

Dioptrics,  that  branch  of  the  science  of  vision  which  relates  to  the 
transmission  of  the  rays  of  light  through  transparent  bodies. 
Greek. 

Dissonance,  in  music,  sounds  which  do  not  harmonize,  but  are  harsh 
and  disagreeable  to  the  ear.  Latin. 

Distraction,  tendency  in  different  directions.    Latin. 

Divergent,  straight  lines  gradually  removing  farther  and  farther  from 
each  other.  See  Convergent.  Latin. 

Diving-hell,  a  machine  of  wood,  glass,  or  metal,  in  form  of  a  bell,  for 
the  purpose  of  enabling  persons  employed  in  certain  kinds  of  fishery, 
and  in  recovering  goods  lost  by  shipwreck,  to  descend  and  remain 
with  safety  under  water. 

Divisibility,  capability  of  being  divided.    Latin. 

Double-concave,  an  optical  glass"  which  has  both  surfaces  hollowed. 

Double-coiivesr,  an  optical  glass  which  has  both  surfaces  raised. 

Ducat,  a  ducal  coin  of  gold,  current  in  Southern  Europe,  value  about 
two  dollars  and  ten  cents. 

Ductile,  pliant,  easily  drawn  or  spread  out.    Latin. 

E. 

Effulgence,  lustre,  brightness.    Latin. 

Elasticity,  a  power  in  bodies  of  recovering  their  former  situation  as  soon 
as  the  force  is  removed  which  had  changed  it.  Thus,  the  extremities 
of  a  bow  are  brought  nearer  by  drawing  the  string;  but  when  the 
string  is  relaxed,  the  bow,  by  its  elasticity,  is  restored  to  its  natural 
state.  It  is  a  properly  of  air,  as  well  as  of  solid  bodies.  Greek. 

Electricity,  the  disposition  which  certain  bodies  have  of  acquiring,  by 
rubbing,  the  quality  of  attracting  other  bodies,  and  of  emitting 
sparks  of  fire.  It  is  derived  from  a  Greek  word  signifying  amber, 
which  is  one  of  the  substances  endowed  with  the  electrical  virtue. 

Elicit,  to  strike  out  by  force.  Thus,  by  a  sharp  stroke  of  the  steel  on 
flint,  fire  is  elicited.  Latin. 

Elogium,  or  Eulogium,  an  oration  in  praise  of  one  absent  or  dead. 
Greek. 

Elucidation,  the  act  of  explaining  or  rendering  clearer.    Latin. 

Emanat/on,  an  issuing  or  flowing  from  any  substance  as  a  source. 
Latin. 

Emersion,  in  astronomy,  the  reappearance  of  a  star,  planet,  or  satellite, 
after  having  been  obscured  by  the  intervention  of  another  body  inter- 
cepting the  light.  Latin. 


428  GLOSSARY. 

Emission,  the  act  of  sending  out,  or  giving  vent.    Latin. 

Encyclopedia,  the  whole  circle  of  science ;  a  universal  scientific  dic- 
tionary. Greek. 

Epicurean,  belonging  to  the  doctrine  or  philosophy  of  Epicurus ;  accord- 
ing to  which  man's  duty  and  happiness  are  made  to  consist  in  rea- 
sonable indulgence;  it  has  become  descriptive  of  refined  luxury. 

Equator,  an  imaginary  great  circle,  equally  distant  from  both  poles,  sur- 
rounding the  globe  from  east  to  west,  and  dividing  it  into  the  North- 
ern and  Southern  hemispheres.  On  maps  the  degrees  of  longitude 
are  marked  on  it,  from  1  to  180  east  and  west  of  the  first  meridian. 
It  is  by  way  of  distinction  called  the  LINK.  Latin. 

Equidistant,  at  equal  distances.    Latin. 

Equilibrium,  exactness  of  balance  or  counterpoise.  Latin.  The  abla- 
tive with  the  preposition  is  adopted  into  our  language,  in  equilibria, 
to  express  perfectness  of  equality  in  opposed  weights. 

Equinox,  the  equalization  of  day  and  night  which  takes  place  twice 
every  year,  the  21st  of  March  and  the  21st  of  September,  when  the 
sun,  in  his  alternate  progress  from  north  to  south,  and  from  south  to 
north,  passes  directly  over  the  equator,  which  is  likewise,  for  this 
reason,  frequently  denominated  the  Equinoctial  Line.  Latin. 

Era,  an  important  event  or  period  of  time.    Latin. 

Erudition,  extensive  and  profound  leaining.    Latin. 

Ether,  the  most  subtile  and  attenuated  of  all  fluids.     Greek. 

Evaporation,  the  act  of  flying  off  in  fumes  or  vapour; 

Exhalation,  a  word  of  the  same  import  with  the  preceding;  evaporation 
may  be  considered  as  the  cause,  and  exhalation  as  the  effect. 
Latin. 

Expansibility,  capability  of  being  spread  out,  and  of  occupying  a  larger 
space.  Latin. 

Experiment,  a  practical  trftil  made  to  ascertain  any  fact.    Latin. 

Extension,  space  over  which  matter  is  diffused;  size,  magnitude. 
Latin. 

Extraneous,  not  belonging  to.    Latin. 

F. 

Fathom,  a  measure  of  length  containing  six  feet.    Saxon. 

Fibre,  a  small  thread.  In  anatomy,  fibres  are  long,  slender,  whitish 
filaments,  variously  interwoven,  which  form  the  solid  parts  of  an 
animal  body.  Latin. 

Fifth,  in  music,  one  of  the  harmonic  intervals  or  concords,  and  the  third 
in  respect  of  harmony,  or  agreeableness  to  the  ear.  It  is  so  called 
because  it  contains  five  tones  or  sounds  between  its  extremes.  See 
vol.  i.  let.  vii. 

Filament,  the  same  with  fibre.    Latin, 

Fluid,  consisting  of  parts  easily  moveable  among  each  other,  as  melted 
metals,  water,  air.  Latin. 

Flux,  in  geography,  the  rising  of  the  tide.    Latin. 

Focus,  in  optics,  the  little  cirde  in  which  rays  of  light  are  collected, 
either  after  passing  through  a  glass,  or  on  being  thrown  back  from 
a  reflector,  and  where  they  exert  their  greatest  power  of  burning. 
Latin. 

Formula,  a  set  or  prescribed  standard ;  a  scheme  for  solving  mathe- 
matical and  algebraical  questions.  Latin. 

Fvrte,  in  music,  forcibly,  in  opposition  to  piano,  softly.    Latin. 


GLOSSARY.  429 

fourth,  in  music,  one  of  the  harmonic  intervals,  and  the  fourth  in  re- 
spect of  agreeableness  to  the  ear.  It  consists  of  two  sounds  blended 
in  the  proportion  of  4  to  3;  that  is,  of  sounds  produced  by  chords 
whose  lengths  are  in  the  proportion  of  4  to  3.  See  vol.  i.  lei.  vi. 
and  vii. 

Friction,  the  act  of  rubbing  one  body  against  another.    Latin. 

Fusible,  that  may  be  melted.    Latin. 

G. 

Gamut,  the  scale  of  musical  notes.    Italian. 

Genus,  kind,  general  class  containing  several  species,  which  again  con- 
tain many  individuals.  Thus,  dog  is  a  genus,  greyhound  is  a 
species,  and  Lightfoot  an  individual.  Latin.  The  plural  is  genera. 

Geography,  a  description  of  the  earth.    Greek. 

Geometry,  the  science  of  quantity,  magnitude  or  extension  abstractly 
considered.  Greek. 

Glaucous,  azure-coloured.    Greek. 

Globule,  small  globe  ;  little  particles  of  a  spherical  form.    Latin. 

Gradation,  regular  progress  from  one  step  to  another.    Latin. 

Gravity,  weight ;  in  the  system  of  the  universe,  that  principle  in  all 
bodies  which  attracts  them  towards  each  other.  Latin. 

Groove,  a  channel  cut  out  in  a  hard  body  with  a  tool,  fitted  to  another 
body  which  is  designed  to  move  in  it. 

H. 

Harmony,  in  music,  a  combination  of  sounds  perfectly  adapted  to  each 
other,  so  as  to  produce  a  pleasing  effect  on  the  ear.  Greek. 

Hemisphere,  one-half  of  a  globe.    Greek. 

Heterogeneous,  composed  of  dissimilar  or  discordant  parts ;  it  is  the 
opposite  of  homogeneous,  which  signifies,  composed  of  things  sim- 
ilar. Greek. 

Horizon,  the  line  which  terminates  the  view.  In  geography,  an  imagi- 
nany  circle  encompassing  the  globe,  and  dividing  it  into  the  upper 
and  under  hemispheres.  To  a  person  placed  at  either  of  the  poles 
the  equator  would  be  the  real  horizon.  The  sensible  horizon  is  the 
circle  visibly  surrounding  us,  where  the  sky  and  the  earth  appear  to 
meet.  Greek. 

Humidity,  moisture.    Latin. 

Hydrography,  a  description  of  that  part  of  our  globe  which  consists  of 
water.  Greek. 

Hypothesis,  a  proposition  or  doctrine  supposed  to  be  true,  but  not  yet 
confirmed  by  irresistible  argument  or  satisfying  experiment.  Greek. 

I. 

Idealist,  a  kind  of  philosopher,  who  denies  the  existence  of  matter,  and 
reduces  every  thing  to  idea  or  mental  image.  Greek. 

Illimitable,  what  admits  of  no  bound.    Latin. 

Illumination,  the  act  of  diffusing  light.    Latin. 

Illusion,  what  deceives  by  a  false  appearance.    Latin. 

Immaterial,  in  philosophy,  not  consisting  of  body  or  matter.    Latin. 
lersion,  in  astronomy,  the  disappearance  of  a  celestial  body  by  the 
interception  of  its  light  by  another  body.    Latin. 


430  GLOSSARY. 

Impenetrability,  that  property  of  all  bodies  in  virtue  of  which  no  two 
can  occupy  the  same  space  at  the  same  time.  Latin. 

Impulsion,  the  agency  of  one  body  in  motion  upon  another.    Latin. 

Immutability,  the  quality  of  being  charged  .upon,  or  ascribed  unto 
Latin. 

Incidence,  the  direction  in  which  one  body  falls  upon  or  strikes  another ; 
and  the  angle  formed  by  that  line  and  the  plane  struck  upon  is  called 
the  angle  of  incidence.  Latin. 

Index,  the  fore-finger ;  any  instrument  that  points  out  or  indicates. 
Latin. 

Individual,  one  separate,  distinct,  undivided  whole. 

Inertia,  that  quality  of  bodies  in  virtue  of  which  they  are  disposed  to 
continue  in  a  state  of  rest  when  at  rest,  or  of  movion  when  in  mo- 
tion ;  and  which  can  be  overcome  only  by  a  power  not  in  the  body 
itself.  Latin, 

Infinity,  boundlessness,  applied  equally  to  space,  number,  and  duration  • 
in  injinitum,  without  limit,  without  end.  Latin. 

Inflection,  the  act  of  bending  or  turning.    Latin. 

Inherent,  naturally  belonging  to,  and  inseparable  from.    Latin. 

Intellectual,  relating  to  the  understanding,  mental.    Latin. 

Intensity,  the  state  of  being  stretched,  heightened,  affected  to  a  very 
high  degree.  Latin. 

Interception,  the  cutting  off  or  obstruction  of  communication.    Latin. 

Intersect,  mutually  to  cut  or  divide.    Latin. 

Interstice,  the  space  between  one  thing  and  another. 

Inverse,  having  changed  places,  indirect,  turned  upside  down.    Latin. 

Iris,  the  circle  round  the  pupil  of  the  eye.    Latin. 

L. 

Labyrinth,  maze,  inextricable  difficulty  or  perplexity.    Latin. 

Latitude,  in  geography,  distance  of  places  from  the  equator  measured 
on  the  meridian,  in  degrees  and  minutes.  The  degree  contains 
about  69  English  miles,  and  a  minute  is  the  sixtieth  part  of  a  de- 
gree. The  highest  possible  degree  of  latitude  is  at  the  poles,  eacb 
being  90  degrees  from  the  equator.  Latin. 

Lens,  a  glass  for  assisting  vision,  or  deriving  fire  from  the  collected 
rays  of  the  sun. 

Lenticular,  having  the  form  of  a  lens. 

Level,  being  at  the  same  height  in  all  parts.     Saxon. 

Literati,  the  learned  ;  the  plural  of  the  Latin  word  literalus,  a  learned 

man. 

•  Logic,  the  art  of  right  reasoning,  for  the  purpose  of  investigating  and 
communicating  useful  truth.  Greek. 

Longitude,  in  geography,  the  angle  which  is  formed  by  the  meridian  of 
any  place  and  the  first  meridian,  measured  in  degrees  and  minutes 
on  the  equator.  Latin. 

Lunar  tide,  the  flowing  and  ebbing  of  the  tide  relatively  to  the  moon. 
Latin. 

Lymphatic  vessels,  slender  transparent  tubes  through  which  lymph,  or 
a  clear  colourless  fluid,  is  conveyed. 

M. 

Magnet,  or  loadstone,  an  ore  of  iron  which  attracts  iron  and  steel,  and 
gives  polarity  to  a  needle.  Art  has  been  enabled,  by  means  of  bars 


GLOSSARY.  431 

of  steel,  successfully  to  imitate  the  natural  magnet  or  loadstone. 
Latin. 

Magnitude,  greatness,  bulk,  extension.    Latin. 

Manichean,  one  of  a  sect  who  maintained  the  existence  of  a  supreme  evil 
spirit. 

Major,  in  logic,  the  first  proposition  of  a  syllogism,  containing  some 
general  assertion  or  denial ;  as,  all  men  are  mortal ;  no  man  is  per- 
fect. Latin. 

Materialist,  one  who  denies  the  existence  of  spiritual  substances. 
Latin. 

Mathematics,  the  science  which  has  for  its  object  every  thing  capable  of 
being  measured  or  numbered.  Greek. 

Mean,  or  Medium,  in  physics,  that  which  intervenes  between  one  sub- 
stance and  another ;  in  lo«ic,  an  intermediate  proposition  employed 
to  lead  to  a  fair  and  just  conclusion.  Latin. 

Mechanics,  the  geometry  of  motion;  the  science  of  constructing  moving 
machinery.  Greek. 

Membrane,  a  web  of  various  fibres  interwoven,  for  wrapping  up  certain 
parts  of  vegetable  and  animal  bodies.  Latin. 

Meniscus  lens,  in  optics,  a  glass  which  is  convex  on  one  surface,  and 
concave  on  the  other,  the  two  surfaces  approaching  at  the  edges. 

Mephites,  poisonous,  ill-scented  vapour.    Latin. 

Mercury,  the  chymical  name  of  the  fluid  commonly  called  quicksilver. 

Meridian,  in  geography,  a  great  circle  encompassing  the  globe  in  the 
direction  of  South  and  North,  and  dividing  it  into  eastern  and 
western  hemispheres.  The  degrees  of  latitude,  from  the  equator  tc 
both  poles,  are  marked  on  this  circle.  Every  spot  of  the  globe 
comes  to  its  meridian  once  in  every  twenty-four  hours,  that  is,  has 
its  instant  of  noon.  Latin. 

Metaphysics,  otherwise  called  Ontology,  the  science  of  the  affections  of 
beings  in  general.  It  employs  abstract  reasoning.  See  Abstract. 
Greek. 

Meteorology,  the  science  of  meteors,  that  is,  of  bodies  floating  in  the  air, 
and  quickly  passing  away.  Greek. 

Microscope,  an  optical  instrument,  which,  by  means  of  a  greatly-mag- 
nifying glass,  renders  distinctly  visible  objects  too  minute  for  the 
unassisted  eye.  Greek. 

Minor,  in  logic,  the  second,  or  particular  proposition  of  a  syllogism ;  for 
example,  in  this  syllogism, — 

All  men  are  mortal : 

But,  The  king  is  a  man ; 

Therefore,  The  king  is  mortal. 

the  first  proposition, "  All  men  are  mortal,"  is  the  major ;  the  second, 
"The  king  is  a  man,"  is  the  minor;  and  these  two  are  called  the 
premises;  the  third,  "  the  king  is  mortal,"  is  the  conclusion.  Latin. 

Mobility,  easiness  of  being  moved.    Latin. 

Mode,  in  logic,  particular  form  or  structure  of  argument.    Latin. 

Monad,  a  minute  particle  of  matter  which  admits  of  no  further  subdi- 
vision. Greek. 

Monochord,  a  musical  instrument  of  one  string.    Greek. 

Myops,  short-sighted.    Greek. 

N. 

ffadir,  the  point  in  the  heavens  directly  under  foot.    Arabic. 
Navigation,  the  art  of  sailing.    Latin. 


432  GLOSSARY. 

Negation,  denial,  the  opposite  of  affirmation.    Latin. 
Notion,  thought;  representation  of  any  thing  formed  by  the  mind. 
Latin. 

o. 

Objective  lens,  in  optics,  that  glass  of  a  telescope  which  is  turned  to  the 

object  or  thing  looked  at.    Latin. 

Oblique,  not  direct,  not  perpendicular,  not  parallel.    Latin. 
Observatory,  an  edifice  reared  for  the  purpose  of  astronomical  observa- 
tions.   Latin. 

Occult,  secret,  unknown,  undiscoverable.    Latin.  • 
Octave,  in  music,  a  regular  succession  of  notes  from  one  to  eight ;  the 

first  and  the  eighth  having  the  same  name  and  emitting  the  same 

sound.    Latin. 
Ocular  lens,  in  optics,  that  glass  of  a  telescope  which  is  applied  to  the 

eye.    Latin. 

Opaque,  impervious  to  the  rays  of  light,  not  transparent.    Latin. 
Optics,  the  science  of  the  nature  and  laws  of  vision,  or  sight.    Greek. 
Orb,  sphere,  heavenly  globular  body.    Latin. 
Orbit,  the  circular  path  in  which  a  planet  moves  round  the  sun  or  another 

planet.    Latin. 
Oscillation,  alternate  moving  backward  and  forward,  like  the  pendulum 

of  a  clock.    Latin. 

P. 

Paradox,  a  tenet  which  exceeds  or  contradicts  received  opinion ;  affirma- 
tion contrary  to  appearance.  Greek. 

Parallel  lines,  in  geometry,  lines  which  through  the  whole  of  their  length 
maintain  the  same  distance.  They  are  the  opposite  of  convergent 
and  divergent.  Latin. 

Parallelism,  stale  of  being  parallel. 

Parallelogram,  a  geometrical  figure  of  four  sides,  having  this  property, 
that  the  opposite  sides  are  equal  and  parallel,  and  the  opposite 
angles  equal.  Greek. 

Pellvcid,  transmitting  the  rays  of  light,  transparent.    Latin. 

Pendulum,  a  body  suspended  so  as  to  swing  backwards  and  forwards 
without  obstruction.  A  pendulum  is  generally  used  for  measuring 
time ;  the  great  perfection  of  such  an  instrument  is,  that  every 
vibration  or  swing  shall  be  performed  in  exactly  the  same  quan- 
tity of  time.  Latin. 

Perception,  the  power  of  perceiving,  knowledge,  consciousness.    Latin. 

Permeable,  susceptible  of  being  passed  through.    Latin. 

Perpendicular,  in  geometry,  one  line  standing  on  another,  or  on  a  hori- 
zontal plane,  without  the  slightest  inclination  to  one  side  or  the 
other,  and  forming  right-angles  with  the  horizontal  line  or  plane. 
Latin. 

Phalanx,  a  military  force  closely  imbodied.    Latin. 

Phasis,  appearance  presented  by  the  changes  of  a  heavenly  body,  par- 
ticularly those  of  the  moon.  The  plural  phases  is  adopted  in  our 
language.  Greek  and  Latin. 

Phenomenon,  striking  appearance  in  nature.  The  plural  phenomena  is 
in  common  use.  Greek. 

Philosophy,  knowledge  natural  or  moral ;  system  in  correspondence  to 


GLOSSARY.  433 

which  important  truths  are  explained ;  academical  course  of  science. 

Greek. 

Physics,  the  science  of  nature,  natural  philosophy.     Greek. 
Piano,  in  music,  soflly,  delicately,  opposite  to  forte.    Italian. 
Piston,  the  moveable  circular  substance  fitted  to  the  cavity  of  a  tube,— 

such  as  a  pump  or  syringe,— for  the  purpose  of  suction,  expulsion, 

or  condensing  of  fluids.    French. 
Planet,  a  wandering  star ;   those  heavenly  bodies,  our  globe  being  one, 

which  perform  their  courses  round  the  sun  are  called  planets.   Greek. 
Plano-concave,  in  optics,  a  glass  which  has  one  surface  plane,  and  the 

other  hollow.    Latin. 
Plano-convex,  an  optical  glass  which  has  one  surface  plane,  and  the 

other  raised.    Latin. 

Plenum,  space  filled  with  substance.    Latin. 

Plumb-line,  a  weight  appended  to  a  string,  for  the  purpose  of  ascertain- 
ing perpendicularity. 

Polar  Circles,  circles  parallel  to  the  equator  and  the  tropics,  at  the  dis- 
tance of  twenty-three  degrees  and  a  half  each  from  its  respective 

pole.     Latin. 

Polarity,  tendency  towards  the  pole.    Latin. 
Polygon,  a  figure  having  many  sides  and  angles.    Greek. 
Polytheism,  the  doctrine  of  a  plurality  of  gods.    Greek. 
Porous,  full  of  small  minute  spaces.    Greek. 
Presbytes,  far-sighted.     Greek. 
Prescience,  foreknowledge.    Latin. 
Predicate,  in  logic,  what  is  affirmed  of  the  subject,  as,  man  is  rational. 

Latin. 

Predilection,  preference  given  from  preconceived  affection.    Latin. 
Pre-established  Harmony,  the  metaphysical   doctrine  of  an  original 

adaptation  of  mind  to  matter,  by  a  creative  act  of  the  Supreme 

Will,  in  virtue  of  which  every  human  action  is  performed. 
Prism,  a  triangular  optical  instrument  of  glass,  contrived  for  the  purpose 

of  making  experiments  with  the  rays  of  light.    Greek. 
Problem,  a  proposition  announcing  something  to  be  first  perfoimed,  and 

then  demonstrated.    Greek. 

Proboscis,  Che  snout  or  trunk  of  an  elephant  or  other  animal.    Latin. 
Prominent,  jutting  out,  projecting  forward.     Latin. 
Proposition,  a  point  advanced  or  affirmed  with  a  view  to  proof.    Latin. 
Proximity,  nearness.     Latin. 

Pupil,  in  optics,  the  apple  or  central  opening  of  the  eye.    Latin. 
Pyrometer,  a  machine  contrived  to  ascertain  the  degree  of  the  expansion 

of  solid  bodies  by  the  force  of  fire.    Greek. 
Pyrrhonist,  a  universal  doubter  and  unbeliever ;  derived  from  Pyrrhus. 

Q. 

Quadrant,  the  fourth  part  of  a  circle ;  an  instrument  of  that  form,  con- 
trived to  measure  altitudes  and  distances  of  celestial  bodies.  Latin. 

Quadrilateral,  consisting  of  four  sides.    Latin. 

Quotient,  in  arithmetic,  the  number  resulting  from  the  division  of  two 
numbers  which  measure  each  other.  Thus,  on  dividing  36  by  4  w0 
have  a  quotient  of  9. 

VOL.  II.— 0  o 


484  GLOSSARY. 

R. 

Radius,  in  English  ray,  a  straight  line  drawn  from  the  centre  of  a  circle 
or  sphere  to  the  circumference.  The  plural  radii  is  in  use.  Latin. 

Rarefaction,  the  rendering  of  a  substance  thinner,  more  transparent;  it 
is  the  opposite  of  condensation.  Latin. 

Ratio,  proportion.    Latin. 

Ratiocination,  a  process  of  reasoning,  a  deduction  of  fair  conclusions 
from  admitted  premises.  Latin. 

Recipient,  that  which  receives  and  contains.    Latin. 

Reciprocally,  mutually,  interchangeably.    Latin. 

Rectangular,  containing  one  or  more  right-angles.  A  right-angle  con- 
sists of  90  degrees. 

Rectilinear,  consisting  of  straight  lines.    Latin. 

Reflection,  in  catoptrics,  the  sending  back  of  the  rays  of  light  from  an 
opaque  surface.  Latin. 

Reflux,  the  ebbing,  or  flowing  back  of  the  tide.    Latin. 

Refraction,  in  dioptrics,  the  deviation  of  a  ray  of  light  on  passing  ob- 
liquely from  one  medium  into  another  of  a  different  density,  as 
from  air  into  water  or  glass.  Latin. 

Refrangibility,  disposition  to  leave  the  direct  course,  capability  of  being 
broken  or  refracted.  Latin. 

Refrangent  medium,  that  which  alters  or  breaks  off  the  course  of  rays. 
Latin. 

Reminiscence,  the  power  of  recollection,  memory.    Latin. 

Repulsion,  the  act  or  power  of  driving  back.     Latin. 

^Resinous,  consisting  of,  or  similar  to,  resin,  a  principle  contained  in  cer 
tain  vegetables.  Latin. 

Resonance,  sound  repeated.    Latin. 

Respiration,  the  act  of  breathing.    Latin. 

Reticulated,  formed  like  a  net.    Latin. 

Retina,  the  delicate  net-like  membrane  at  the  bottom  of  the  eye,  on  which 
are  painted  the  images  of  the  objects  which  we  contemplate.  Latin. 

Retrograde,  moving  in  a  backward  direction.    Latin. 

Reverberation,  the  act  of  beating  or  driving  back.    Latin. 

Revery,  loose,  wild,  irregular  meditation. 

S. 

Satellite,  an  inferior  attendant  planet  revolving  round  a  greater.    Latin. 

Scalpel,  a  surgical  dissecting-knife.     Latin. 

Science,  knowledge :  grammar,  rhetoric,  logic,  arithmetic,  music,  geom- 
etry, astronomy,  have  been  styled  the  seven  liberal  arts. 

Segment,  in  geometry,  part  of  a  circle  formed  by  a  straight  line  drawn 
from  one  extremity  of  any  arc  to  the  other,  and  the  part  of  the  cir- 
cumference which  constitutes  that  arc.  The  straight  line  is  de- 
nominated the  chord  of  the  arc,  from  its  resemblance  to  a  bowstring. 

Semicircle,  the  half  of  a  circle  ;  the  segment  formed  by  the  diameter  as 
the  chord,  and  one-half  the  circumference  as  the  arc.  Latin. 

Semitone,  in  music,  half  a  tone,  the  least  of  all  intervals  admitted  into 
modern  music.  The  semitone  major  is  the  difference  between  the 
greater  third  and  the  fourth  ;  its  relation  is  as  15  to  16.  The  semi- 
tone minor  is  the  difference  between  the  greater  third  and  the  lesser 
third,  and  its  relation  is  as  24  to  25.  Latin. 

Sensation,  perception  by  means  of  the  senses.    Latin. 


GLOSSARY.  435 

Series,  regular,  settled,  proportional  order  of  progression,  as,  in  num- 
bero,  9,  18,  27,  36,  45,  54,  63,  are  in  a  series.  The  word  is  the  same 
singular  and  plural.  Latin. 

Seventh,  in  music,  the  inverted  discordant  interval  of  the  second,  called 
by  the  ancients  Heptachordon,  because  it  is  formed  of  seven  sounds. 
There  are  four  sorts  of  the  seventh,  of  which  the  following  are  the 
proportions :  as  5  to  9,  as  8  to  15,  as  75  to  128,  as  81  to  160.  It  is 
harsh  and  un  harmonious. 

Solar  tide,  the  flux  and  reflux  of  the  tide  relatively  to  the  sun.    Latin. 

Solution,  demonstration,  clearing  up  of  intricacy  or  difficulty.    Latin. 

Sonorous,  emitting  loud  or  shrill  sounds.    Latin. 

Sptc/es,  kind,  sort,  class.  See  Genus.  It  is  the  same  in  singular  and 
plural.  Latin. 

Spectrum,  an  image,  a  visible  form.    Latin. 

Sphere,  globe.    Greek. 

Spheroid,  approaching  to  the  form  of  a  sphere.  If  lengthened,  it  is 
called  a  prolate,  if  flattened,  an  oblate  spheroid.  Greek. 

Spiritual,  not  consisting  of,  but  distinct  from,  matter  or  body.    Latin. 

Sublime,  elevated  in  place.  In  chymistry,  raised  by  the  force  of  fire. 
Latin. 

Subterfuge,  a  paltry  escape  or  evasion.    Latin. 

Subterraneous,  under  the  surface  of  the  ground.    Latin. 

Subtile,  thin,  not  dense,  not  gross.    Latin. 

Superficial,  external,  extended  along  the  surface.    Latin. 

Supernatural,  what  is  above  or  beyond  the  ordinary  course  of  nature. 
Latin. 

Surface,  in  geometry,  length  and  breadth  without  thickness. 

Syllogism,  in  logic,  an  argument  consisting  of  three  propositions.  For 
example,  Every  virtue  is  commendable  ;  honesty  is  a  virtue  ;  there- 
fore honesty  is  commendable.  See  Major  and  Minor.  Greek. 

System,  a  scheme  of  combination  and  arrangement,  which  reduces  many 
things  to  a  regular  connexion,  dependence,  and  co-operation.  Greek. 

T. 

Tangent,  in  geometry,  a  straight  line  touching  a  circle  externally  in  a 

single  point.    Latin. 
Telescope,  an  optical  instrument  designed,  by  the  magnifying  power  of 

glasses,  to  represent  distant  bodies  as  much  nearer.    Greek. 
Temperament,  state  of  body  or  mind  as  produced  by,  or  depending  upon, 

the  predominancy  of  a  particular  quality.    Latin. 
Tension,  the  state  of  being  stretched  out,  wound  up,  distended.    Latin 
Tenuity,  thinness,  delicate  fineness.    Latin. 

Term,  descriptive  name  or  phrase,  component  part,  condition.    Latin. 
Terraqueous,  consisting  of  land  and  water.    Latin. 
Theology,  systematic  divinity.    Greek. 

Theorem,  a  proposition  announced  for  demonstration.    Greek. 
Theory,  a  doctrine  contemplated  and  conceived  in  the  mind,  but  not  yet 

confirmed  by  irresistible  argument  or  satisfying  experiment.    Greek. 
TJiermometer,  an  instrument  contrived  to  measure  the  heat  of  the  air  or 

other  body  by  means  of  the  rising  or  falling  of  a  fluid  in  a  glass. 

Greek. 
Third,  in  music,  the  first  of  the  two  imperfect  concords,  so  called  because 

its  interval  is  always  composed  of  two  degrees  or  three  diatonic 

Bounds.    The  tierce  major,  or  greater  third,  is  represented  in  num- 


436  GLOSSARY. 

bers  by  the  ratio  of  4  to  5 ;  and  the  lesser  by  the  relation  of  5  to  6 
See  vol.  i.  let.  vi.  and  vii. 

Tide,  the  alternate  rising  and  fallingof  the  water  in  rivers  and  along  the 
shores  of  the  sea.  Saxon  and  Dutch. 

Tone,  in  music,  the  degree  of  elevation  which  the  voice  assumes,  and  to 
which  instruments  are  adapted,  in  order  to  the  harmonious  execu- 
tion of  a  musical  composition  ;  a  pitch-pipe.  Latin  and  Greek. 

Transit,  in  astronomy,  the  passing  of  one  heavenly  body  over  the  disk 
of  another.  Latin. 

Transmission,  the  sending  of  one  body  or  substance  through  or  to  an- 
other. Latin. 

Transparent,  clear,  permeable  to  light,  as  air,  water,  glass.    Latin. 

Transverse,  in  a  cross  direction.    Latin. 

Triangle,  a  geometrical  figure  consisting  of  three  sides  and  three  angles. 
Latin. 

Tube,  a  pipe,  a  long  hollow  body.    Latin. 

Tunicle,  a  small  coat  or  covering.    Latin. 

u. 

Ultimate,  final,  beyond  which  there  is  no  farther  progress.    Latin. 
Unison,  emission  of  the  same  or  harmonious  sounds.    Latin. 
Untenable,  what  cannot  be  maintained  or  supported. 

T- 

Vacuum,  empty  space.    Latin. 

Valve,  a  door,  a  moveable  membrane  in  the  vessels  of  an  animal  body, 
and  imitated  by  art  in  the  construction  of  various  machines,  which 
opens  for  giving  passage  to  fluids  in  one  direction,  but  shuts  to 
oppose  their  return  through  the  same  passage.  Latin. 

Velocity,  speed,  swiftness  of  motion.    Latin. 

Vertical,  perpendicular,  upright.  Vertical  angles,  in  geometry,  are 
those  formed  by  the  intersection  of  two  straight  lines,  in  whatever 
direction,  making  four  in  all  at  the  point  of  intersection,  and  of 
which  the  opposite  two  and  two  are  equal.  Latin. 

Vibration,  motion  backwards  and  forwards.    Latin. 

Visual,  relating  to  vision  or  sight,  belonging  to  the  eye.    Latin. 

Vitreous,  composed  of  or  resembling  glass.    Latin. 

Vivid,  lively,  brisk,  sprightly.    Latin. 

w. 

Waning,  gradual  diminution  of  apparent  magnitude  and  light.    Saxon. 
Waxing,  gradual  increase  of  apparent  magnitude  and  light,  particularly 

of  the  moon.    Saxon  and  Danish. 
Wind-gun,  a  gun  which  forcibly  emits  a  ball  by  means  of  compressed 

air  or  wind. 

z. 

Zenith,  the  point  in  the  heavens  exactly  over-head  j  the  opposite  of 
Nadir, 


